Handbook Of Differential Geometry Volume 1

Author : F.J.E. Dillen,L.C.A. Verstraelen
Publisher : Elsevier
Page : 1067 pages
File Size : 51,6 Mb
Release : 1999-12-16
Category : Mathematics
ISBN : 9780080532837

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Handbook of Differential Geometry, Volume 1 by F.J.E. Dillen,L.C.A. Verstraelen Pdf

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. 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.

Author : Franki J.E. Dillen,Leopold C.A. Verstraelen
Publisher : Elsevier
Page : 574 pages
File Size : 45,9 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

Author : F.J.E. Dillen,L.C.A. Verstraelen
Publisher : North Holland
Page : 1053 pages
File Size : 42,5 Mb
Release : 1999-12-30
Category : Mathematics
ISBN : 0444822402

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Handbook of Differential Geometry by F.J.E. Dillen,L.C.A. Verstraelen Pdf

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. 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.

Author : Lizhen Ji
Publisher : Unknown
Page : 704 pages
File Size : 40,9 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015080827705

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Handbook of Geometric Analysis by Lizhen Ji Pdf

"Geometric Analysis combines differential equations with differential geometry. An important aspect of geometric analysis is to approach geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Amperè equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications. This handbook of geometric analysis--the first of the two to be published in the ALM series--presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas."--Back cover.

Author : Shoshichi Kobayashi,Katsumi Nomizu
Publisher : John Wiley & Sons
Page : 356 pages
File Size : 41,8 Mb
Release : 1996-02-22
Category : Mathematics
ISBN : 9780471157335

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Foundations of Differential Geometry, Volume 1 by Shoshichi Kobayashi,Katsumi Nomizu Pdf

This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.

Author : Andrew McInerney
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 45,7 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.

Author : Anonim
Publisher : Elsevier
Page : 1017 pages
File Size : 47,6 Mb
Release : 2001-08-15
Category : Mathematics
ISBN : 9780080532806

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Handbook of the Geometry of Banach Spaces by Anonim Pdf

The Handbook presents an overview of most aspects of modernBanach space theory and its applications. The up-to-date surveys, authored by leading research workers in the area, are written to be accessible to a wide audience. In addition to presenting the state of the art of Banach space theory, the surveys discuss the relation of the subject with such areas as harmonic analysis, complex analysis, classical convexity, probability theory, operator theory, combinatorics, logic, geometric measure theory, and partial differential equations. The Handbook begins with a chapter on basic concepts in Banachspace theory which contains all the background needed for reading any other chapter in the Handbook. Each of the twenty one articles in this volume after the basic concepts chapter is devoted to one specific direction of Banach space theory or its applications. Each article contains a motivated introduction as well as an exposition of the main results, methods, and open problems in its specific direction. Most have an extensive bibliography. Many articles contain new proofs of known results as well as expositions of proofs which are hard to locate in the literature or are only outlined in the original research papers. As well as being valuable to experienced researchers in Banach space theory, the Handbook should be an outstanding source for inspiration and information to graduate students and beginning researchers. The Handbook will be useful for mathematicians who want to get an idea of the various developments in Banach space theory.

Author : Victor Andreevich Toponogov
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 44,6 Mb
Release : 2006-09-10
Category : Mathematics
ISBN : 9780817644024

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Differential Geometry of Curves and Surfaces by Victor Andreevich Toponogov Pdf

Central topics covered include curves, surfaces, geodesics, intrinsic geometry, and the Alexandrov global angle comparision theorem Many nontrivial and original problems (some with hints and solutions) Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels

Author : Wolfgang Kühnel
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 45,9 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839881

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Differential Geometry by Wolfgang Kühnel Pdf

Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in I\!\!R^3 that arise in calculus. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas. With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces. An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces. The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics. There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.

Author : Shoshichi Kobayashi
Publisher : Princeton University Press
Page : 317 pages
File Size : 52,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400858682

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Differential Geometry of Complex Vector Bundles by Shoshichi Kobayashi Pdf

Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Marcel Berger,Bernard Gostiaux
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210337

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Differential Geometry: Manifolds, Curves, and Surfaces by Marcel Berger,Bernard Gostiaux Pdf

This book consists of two parts, different in form but similar in spirit. The first, which comprises chapters 0 through 9, is a revised and somewhat enlarged version of the 1972 book Geometrie Differentielle. The second part, chapters 10 and 11, is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of physics. Geometrie Differentielle was based on a course I taught in Paris in 1969- 70 and again in 1970-71. In designing this course I was decisively influ enced by a conversation with Serge Lang, and I let myself be guided by three general ideas. First, to avoid making the statement and proof of Stokes' formula the climax of the course and running out of time before any of its applications could be discussed. Second, to illustrate each new notion with non-trivial examples, as soon as possible after its introduc tion. And finally, to familiarize geometry-oriented students with analysis and analysis-oriented students with geometry, at least in what concerns manifolds.

Author : Michael Spivak
Publisher : Unknown
Page : 702 pages
File Size : 48,6 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015062882942

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A Comprehensive Introduction to Differential Geometry by Michael Spivak Pdf

Author : Barrett O'Neill
Publisher : Academic Press
Page : 422 pages
File Size : 40,5 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483268118

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Elementary Differential Geometry by Barrett O'Neill Pdf

Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.

Author : Masaaki Umehara,Kentaro Saji,Kotaro Yamada
Publisher : World Scientific
Page : 387 pages
File Size : 46,7 Mb
Release : 2021-11-29
Category : Mathematics
ISBN : 9789811237157

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Differential Geometry Of Curves And Surfaces With Singularities by Masaaki Umehara,Kentaro Saji,Kotaro Yamada Pdf

This book provides a unique and highly accessible approach to singularity theory from the perspective of differential geometry of curves and surfaces. It is written by three leading experts on the interplay between two important fields — singularity theory and differential geometry.The book introduces singularities and their recognition theorems, and describes their applications to geometry and topology, restricting the objects of attention to singularities of plane curves and surfaces in the Euclidean 3-space. In particular, by presenting the singular curvature, which originated through research by the authors, the Gauss-Bonnet theorem for surfaces is generalized to those with singularities. The Gauss-Bonnet theorem is intrinsic in nature, that is, it is a theorem not only for surfaces but also for 2-dimensional Riemannian manifolds. The book also elucidates the notion of Riemannian manifolds with singularities.These topics, as well as elementary descriptions of proofs of the recognition theorems, cannot be found in other books. Explicit examples and models are provided in abundance, along with insightful explanations of the underlying theory as well. Numerous figures and exercise problems are given, becoming strong aids in developing an understanding of the material.Readers will gain from this text a unique introduction to the singularities of curves and surfaces from the viewpoint of differential geometry, and it will be a useful guide for students and researchers interested in this subject.

Author : José Luis Cisneros Molina,Dũng Tráng Lê,José Seade
Publisher : Springer Nature
Page : 616 pages
File Size : 55,6 Mb
Release : 2020-10-24
Category : Mathematics
ISBN : 9783030530617

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Handbook of Geometry and Topology of Singularities I by José Luis Cisneros Molina,Dũng Tráng Lê,José Seade Pdf

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.