Comparison Theorems in Riemannian Geometry PDF Download

Author: Jeff Cheeger
Publisher: Newnes
ISBN: 0720424615
Category : Electronic books
Languages : en
Pages : 184

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Book Description

Author: Jeff Cheeger
Publisher: Newnes
ISBN: 0444107649
Category : Computers
Languages : en
Pages : 183

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Book Description
Comparison Theorems in Riemannian Geometry

Author: Karsten Grove
Publisher: Cambridge University Press
ISBN: 9780521592222
Category : Mathematics
Languages : en
Pages : 280

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Book Description
This is an up to date work on a branch of Riemannian geometry called Comparison Geometry.

Author: Peter Petersen
Publisher: Springer Science & Business Media
ISBN: 1475764340
Category : Mathematics
Languages : en
Pages : 443

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Book Description
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: Takashi Sakai
Publisher: American Mathematical Soc.
ISBN: 9780821889565
Category : Mathematics
Languages : en
Pages : 378

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Book Description
This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.

Author: Jeff Cheeger
Publisher:
ISBN: 9780720424508
Category :
Languages : en
Pages : 174

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Author: Victor Andreevich Toponogov
Publisher: Springer Science & Business Media
ISBN: 0817644024
Category : Mathematics
Languages : en
Pages : 215

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Book Description
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: D. Bao
Publisher: Springer Science & Business Media
ISBN: 1461212685
Category : Mathematics
Languages : en
Pages : 453

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Book Description
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: John M. Lee
Publisher: Springer
ISBN: 3319917552
Category : Mathematics
Languages : en
Pages : 447

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Book Description
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: Isaac Chavel
Publisher: Cambridge University Press
ISBN: 9780521485784
Category : Mathematics
Languages : en
Pages : 402

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Book Description
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.