An Introduction To Riemannian Geometry

Author : Leonor Godinho,José Natário
Publisher : Springer
Page : 467 pages
File Size : 55,8 Mb
Release : 2014-07-26
Category : Mathematics
ISBN : 9783319086668

Get Book

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.

Author : John M. Lee
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 47,9 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227269

Get Book

Riemannian Manifolds by John M. Lee Pdf

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Author : John M. Lee
Publisher : Springer
Page : 437 pages
File Size : 52,9 Mb
Release : 2019-01-02
Category : Mathematics
ISBN : 9783319917559

Get Book

Introduction to Riemannian Manifolds by John M. Lee Pdf

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Author : William Munger Boothby
Publisher : Gulf Professional Publishing
Page : 444 pages
File Size : 46,8 Mb
Release : 2003
Category : Mathematics
ISBN : 0121160513

Get Book

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

Author : D. Bao,S.-S. Chern,Z. Shen
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461212683

Get Book

An Introduction to Riemann-Finsler Geometry by D. Bao,S.-S. Chern,Z. Shen Pdf

This book focuses on the elementary but essential problems in Riemann-Finsler Geometry, which include a repertoire of rigidity and comparison theorems, and an array of explicit examples, illustrating many phenomena which admit only Finslerian interpretations. "This book offers the most modern treatment of the topic ..." EMS Newsletter.

Author : Bernhard Riemann
Publisher : Birkhäuser
Page : 172 pages
File Size : 52,9 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9783319260426

Get Book

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.

Author : Erwin Kreyszig
Publisher : University of Toronto Press
Page : 382 pages
File Size : 53,5 Mb
Release : 1968-12-15
Category : Education
ISBN : 9781487591052

Get Book

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.

Author : Peter Petersen
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 52,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475764345

Get Book

Riemannian Geometry by Peter Petersen Pdf

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialise in Riemannian geometry. Instead of variational techniques, the author uses a unique approach, emphasising distance functions and special co-ordinate systems. He also uses standard calculus with some techniques from differential equations to provide a more elementary route. Many chapters contain material typically found in specialised texts, never before published in a single source. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research - including sections on convergence and compactness of families of manifolds. Thus, this book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject.

Author : Charles Ernest Weatherburn
Publisher : CUP Archive
Page : 214 pages
File Size : 41,5 Mb
Release : 1938
Category : Calculus of tensors
ISBN : 8210379456XXX

Get Book

An Introduction to Riemannian Geometry and the Tensor Calculus by Charles Ernest Weatherburn Pdf

Author : Isaac Chavel
Publisher : Cambridge University Press
Page : 4 pages
File Size : 45,6 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9781139452571

Get Book

Riemannian Geometry by Isaac Chavel Pdf

This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.

Author : Isaac Chavel
Publisher : Cambridge University Press
Page : 402 pages
File Size : 46,6 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 0521485789

Get Book

Riemannian Geometry by Isaac Chavel Pdf

This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry, angles, lengths, areas, and volumes, and those new notions and ideas motivated by curvature itself. Isoperimetric inequalities--the interplay of curvature with volume of sets and the areas of their boundaries--is reviewed along with other specialized classical topics. A number of completely new themes are created by curvature: they include local versus global geometric properties, that is, the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. Also featured is an ambitious "Notes and Exercises" section for each chapter that will develop and enrich the reader's appetite and appreciation for the subject.

Author : John M. Lee
Publisher : Springer
Page : 427 pages
File Size : 54,5 Mb
Release : 2018-08-24
Category : Mathematics
ISBN : 3319917544

Get Book

Introduction to Riemannian Manifolds by John M. Lee Pdf

This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Author : T. J. Willmore
Publisher : Courier Corporation
Page : 336 pages
File Size : 47,9 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486282107

Get Book

An Introduction to Differential Geometry by T. J. Willmore Pdf

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

Author : Luther Pfahler B 1876 Eisenhart
Publisher : Hassell Street Press
Page : 328 pages
File Size : 54,7 Mb
Release : 2021-09-09
Category : Electronic
ISBN : 1013373251

Get Book

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.

Author : Joel W. Robbin,Dietmar A. Salamon
Publisher : Springer Nature
Page : 426 pages
File Size : 43,8 Mb
Release : 2022-01-12
Category : Mathematics
ISBN : 9783662643402

Get Book

Introduction to Differential Geometry by Joel W. Robbin,Dietmar A. Salamon Pdf

This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.