Introduction to Differential Geometry

Introduction to Differential Geometry
Author :
Publisher : Springer Nature
Total Pages : 426
Release :
ISBN-10 : 9783662643402
ISBN-13 : 3662643405
Rating : 4/5 (405 Downloads)

Book Synopsis Introduction to Differential Geometry by : Joel W. Robbin

Download or read book Introduction to Differential Geometry written by Joel W. Robbin and published by Springer Nature. This book was released on 2022-01-12 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Introduction to Differential Geometry Related Books

Introduction to Differential Geometry
Language: en
Pages: 426
Authors: Joel W. Robbin
Categories: Mathematics
Type: BOOK - Published: 2022-01-12 - Publisher: Springer Nature

GET EBOOK

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
An Introduction to Differential Geometry
Language: en
Pages: 338
Authors: T. J. Willmore
Categories: Mathematics
Type: BOOK - Published: 2013-05-13 - Publisher: Courier Corporation

GET EBOOK

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculu
Introduction to Smooth Manifolds
Language: en
Pages: 646
Authors: John M. Lee
Categories: Mathematics
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media

GET EBOOK

Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, exc
Elementary Differential Geometry
Language: en
Pages: 336
Authors: A.N. Pressley
Categories: Mathematics
Type: BOOK - Published: 2013-11-11 - Publisher: Springer Science & Business Media

GET EBOOK

Pressley assumes the reader knows the main results of multivariate calculus and concentrates on the theory of the study of surfaces. Used for courses on surface
First Steps in Differential Geometry
Language: en
Pages: 420
Authors: Andrew McInerney
Categories: Mathematics
Type: BOOK - Published: 2013-07-09 - Publisher: Springer Science & Business Media

GET EBOOK

Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear