عنوان

Aspects of differential geometry I /

(Number (ISBN

1627056629

(Number (ISBN

1627056637

(Number (ISBN

1627057846

(Number (ISBN

9781627056625

(Number (ISBN

9781627056632

(Number (ISBN

9781627057844

Erroneous ISBN

1627056629

Erroneous ISBN

1627057838

Erroneous ISBN

9781627056625

Erroneous ISBN

9781627057837

Title Proper

Aspects of differential geometry I /

General Material Designation

[Book]

First Statement of Responsibility

Peter Gilkey (Univesrity of Oregon, Eugene, OR), JeongHyeong Park (Sungkyunkwan University, Suwon, Korea, Institute for Advanced Study, Seoul, Korea), Ramón Vázquez-Lorenzo (University of Santiago de Compostela, Santiago de Compostela, Spain).

Place of Publication, Distribution, etc.

San Rafael, California :

Name of Publisher, Distributor, etc.

Morgan & Claypool Publishers,

Date of Publication, Distribution, etc.

[2015]

Date of Publication, Distribution, etc.

©2015

Specific Material Designation and Extent of Item

1 online resource (xiii, 140 pages) :

Other Physical Details

illustrations

Series Title

Synthesis lectures on mathematics and statistics,

Volume Designation

#15

ISSN of Series

1938-1751 ;

Text of Note

Includes bibliographical references (pages 131-133) and index.

Text of Note

1. Basic notions and concepts -- 1.1 Metric spaces -- 1.2 Linear algebra -- 1.3 The derivative -- 1.4 The inverse and implicit function theorems -- 1.5 The Riemann integral -- 1.6 Improper integrals -- 1.7 The change of variable theorem -- 2. Manifolds -- 2.1 Smooth manifolds -- 2.2 The tangent and cotangent bundles -- 2.3 Stokes' theorem -- 2.4 Applications of stokes' theorem -- 3. Riemannian and pseudo-Riemannian geometry -- 3.1 The pseudo-Riemannian measure -- 3.2 Connections -- 3.3 The Levi-Civita connection -- 3.4 Geodesics -- 3.5 The Jacobi operator -- 3.6 The Gauss-Bonnet theorem -- 3.7 The Chern-Gauss-Bonnet theorem.

0

Text of Note

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new.

Source for Acquisition/Subscription Address

01307586

Title

Aspects of differential geometry.

International Standard Book Number

9781627056625

Geometry, Differential.

Geometry, Differential.

MATHEMATICS-- Geometry-- General.

MAT-- 012000

Number

Edition

Class number

Book number

Gilkey, Peter B.

Park, Jeonghyeong

Vázquez-Lorenzo, Ramón

Date of Transaction

20200823051202.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y