Differential Geometry Riemannian Geometry

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First Steps in Differential Geometry

Andrew McInerney
First Steps in Differential Geometry Book PDF

Author : Andrew McInerney
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 53,5 Mb
Release : 2013-07-09
Category : Mathematics
ISBN : 9781461477327

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First Steps in Differential Geometry by Andrew McInerney Pdf

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.

On the Hypotheses Which Lie at the Bases of Geometry

Bernhard Riemann
On the Hypotheses Which Lie at the Bases of Geometry Book PDF

Author : Bernhard Riemann
Publisher : Birkhäuser
Page : 172 pages
File Size : 50,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9783319260426

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On the Hypotheses Which Lie at the Bases of Geometry by Bernhard Riemann Pdf

This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.

Introduction to Differential Geometry and Riemannian Geometry

Erwin Kreyszig
Introduction to Differential Geometry and Riemannian Geometry Book PDF

Author : Erwin Kreyszig
Publisher : University of Toronto Press
Page : 382 pages
File Size : 44,7 Mb
Release : 1968-12-15
Category : Education
ISBN : 9781487591052

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Introduction to Differential Geometry and Riemannian Geometry by Erwin Kreyszig Pdf

This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space and to n-dimensional Riemannian geometry. Based on Kreyszig's earlier book Differential Geometry, it is presented in a simple and understandable manner with many examples illustrating the ideas, methods, and results. Among the topics covered are vector and tensor algebra, the theory of surfaces, the formulae of Weingarten and Gauss, geodesics, mappings of surfaces and their applications, and global problems. A thorough investigation of Reimannian manifolds is made, including the theory of hypersurfaces. Interesting problems are provided and complete solutions are given at the end of the book together with a list of the more important formulae. Elementary calculus is the sole prerequisite for the understanding of this detailed and complete study in mathematics.

Global Riemannian Geometry: Curvature and Topology

Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer
Global Riemannian Geometry Curvature and Topology Book PDF

Author : Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer
Publisher : Springer Nature
Page : 121 pages
File Size : 41,5 Mb
Release : 2020-08-19
Category : Mathematics
ISBN : 9783030552930

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Global Riemannian Geometry: Curvature and Topology by Ana Hurtado,Steen Markvorsen,Maung Min-Oo,Vicente Palmer Pdf

This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.

Riemannian Geometry

Wilhelm Klingenberg
Riemannian Geometry Book PDF

Author : Wilhelm Klingenberg
Publisher : Walter de Gruyter
Page : 430 pages
File Size : 43,9 Mb
Release : 1995
Category : Mathematics
ISBN : 3110145936

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Riemannian Geometry by Wilhelm Klingenberg Pdf

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

An Introduction to the Analysis of Paths on a Riemannian Manifold

Daniel W. Stroock
An Introduction to the Analysis of Paths on a Riemannian Manifold Book PDF

Author : Daniel W. Stroock
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 48,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9780821838396

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An Introduction to the Analysis of Paths on a Riemannian Manifold by Daniel W. Stroock Pdf

Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.

Handbook of Differential Geometry

Franki J.E. Dillen,Leopold C.A. Verstraelen
Handbook of Differential Geometry Book PDF

Author : Franki J.E. Dillen,Leopold C.A. Verstraelen
Publisher : Elsevier
Page : 574 pages
File Size : 51,6 Mb
Release : 2005-11-29
Category : Mathematics
ISBN : 0080461204

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Handbook of Differential Geometry by Franki J.E. Dillen,Leopold C.A. Verstraelen Pdf

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research . Extensive bibliography . Dealing with a diverse range of areas . Starting from the basics

A Panoramic View of Riemannian Geometry

Marcel Berger
A Panoramic View of Riemannian Geometry Book PDF

Author : Marcel Berger
Publisher : Springer Science & Business Media
Page : 852 pages
File Size : 50,8 Mb
Release : 2007-06-29
Category : Mathematics
ISBN : 3540653171

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A Panoramic View of Riemannian Geometry by Marcel Berger Pdf

This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS

An Introduction to Riemannian Geometry

Leonor Godinho,José Natário
An Introduction to Riemannian Geometry Book PDF

Author : Leonor Godinho,José Natário
Publisher : Springer
Page : 476 pages
File Size : 53,8 Mb
Release : 2014-07-26
Category : Mathematics
ISBN : 9783319086668

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An Introduction to Riemannian Geometry by Leonor Godinho,José Natário Pdf

Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

Differential and Riemannian Geometry

Detlef Laugwitz
Differential and Riemannian Geometry Book PDF

Author : Detlef Laugwitz
Publisher : Academic Press
Page : 250 pages
File Size : 43,5 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483263984

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Differential and Riemannian Geometry by Detlef Laugwitz Pdf

Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces. The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry. The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations. The book is a valuable reference for researchers interested in differential and Riemannian geometry.

An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

William Munger Boothby
An Introduction to Differentiable Manifolds and Riemannian Geometry Revised Book PDF

Author : William Munger Boothby
Publisher : Gulf Professional Publishing
Page : 444 pages
File Size : 55,6 Mb
Release : 2003
Category : Mathematics
ISBN : 0121160513

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An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised by William Munger Boothby Pdf

The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields

Riemannian Geometry and Geometric Analysis

Jürgen Jost
Riemannian Geometry and Geometric Analysis Book PDF

Author : Jürgen Jost
Publisher : Springer
Page : 697 pages
File Size : 43,7 Mb
Release : 2017-10-13
Category : Mathematics
ISBN : 9783319618609

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Riemannian Geometry and Geometric Analysis by Jürgen Jost Pdf

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research. The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the Bishop-Gromov volume growth theorem which elucidates the geometric role of Ricci curvature. From the reviews:“This book provides a very readable introduction to Riemannian geometry and geometric analysis... With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome.” Mathematical Reviews “For readers familiar with the basics of differential geometry and some acquaintance with modern analysis, the book is reasonably self-contained. The book succeeds very well in laying out the foundations of modern Riemannian geometry and geometric analysis. It introduces a number of key techniques and provides a representative overview of the field.” Monatshefte für Mathematik

Geometry of Manifolds

K. Shiohama
Geometry of Manifolds Book PDF

Author : K. Shiohama
Publisher : Elsevier
Page : 517 pages
File Size : 44,6 Mb
Release : 1989-10-04
Category : Mathematics
ISBN : 9780080925783

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Geometry of Manifolds by K. Shiohama Pdf

This volume contains the papers presented at a symposium on differential geometry at Shinshu University in July of 1988. Carefully reviewed by a panel of experts, the papers pertain to the following areas of research: dynamical systems, geometry of submanifolds and tensor geometry, lie sphere geometry, Riemannian geometry, Yang-Mills Connections, and geometry of the Laplace operator.

Riemannian Geometry

Luther Pfahler B 1876 Eisenhart
Riemannian Geometry Book PDF

Author : Luther Pfahler B 1876 Eisenhart
Publisher : Hassell Street Press
Page : 328 pages
File Size : 45,7 Mb
Release : 2021-09-09
Category : Electronic
ISBN : 1013373251

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Riemannian Geometry by Luther Pfahler B 1876 Eisenhart Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Fundamentals of Differential Geometry

Serge Lang
Fundamentals of Differential Geometry Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 553 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205418

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Fundamentals of Differential Geometry by Serge Lang Pdf

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER