東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Linked to FindBook

Google Book

Amazon

博客來

Differential geometry and homogeneous spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Differential geometry and homogeneous spaces/ by Kai Köhler.
Author:	Köhler, Kai.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2024.,
Description:	x, 292 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Manifolds -- 2 Vector Bundles and Tensors -- 3 Riemannian Manifolds -- 4 The Poincaré-Hopf Theorem and the Chern-Gauß-Bonnet Theorem -- 5 Geodesics -- 6 Homogeneous Spaces -- 7 Symmetric Spaces -- 8 General Relativity -- A Solutions to Selected Exercises.
Contained By:	Springer Nature eBook
Subject:	Geometry, Differential. -
Online resource:	https://doi.org/10.1007/978-3-662-69721-4
ISBN:	9783662697214

Differential geometry and homogeneous spaces
Köhler, Kai.

Differential geometry and homogeneous spaces[electronic resource] /by Kai Köhler. - Berlin, Heidelberg :Springer Berlin Heidelberg :2024. - x, 292 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

1 Manifolds -- 2 Vector Bundles and Tensors -- 3 Riemannian Manifolds -- 4 The Poincaré-Hopf Theorem and the Chern-Gauß-Bonnet Theorem -- 5 Geodesics -- 6 Homogeneous Spaces -- 7 Symmetric Spaces -- 8 General Relativity -- A Solutions to Selected Exercises.

This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity. Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincaré-Hopf and Chern-Gauss-Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material. The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.

ISBN: 9783662697214

Standard No.: 10.1007/978-3-662-69721-4doiSubjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA641

Dewey Class. No.: 516.36

Differential geometry and homogeneous spaces
LDR:02480nmm a2200337 a 4500 001 2380378
003 DE-He213
005 20241029115520.0
006 m d
007 cr nn 008maaau
008 250418s2024 gw s 0 eng d
020 $a 9783662697214 $q (electronic bk.)
020 $a 9783662697207 $q (paper)
024 7 $a 10.1007/978-3-662-69721-4 $2 doi
035 $a 978-3-662-69721-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA641
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
072 7 $a PBMP $2 thema
082 0 4 $a 516.36 $2 23
090 $a QA641 $b .K79 2024
100 1 $a Köhler, Kai. $3 3733792
245 1 0 $a Differential geometry and homogeneous spaces $h [electronic resource] / $c by Kai Köhler.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2024.
300 $a x, 292 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 2191-6675
505 0 $a 1 Manifolds -- 2 Vector Bundles and Tensors -- 3 Riemannian Manifolds -- 4 The Poincaré-Hopf Theorem and the Chern-Gauß-Bonnet Theorem -- 5 Geodesics -- 6 Homogeneous Spaces -- 7 Symmetric Spaces -- 8 General Relativity -- A Solutions to Selected Exercises.
520 $a This textbook offers a rigorous introduction to the foundations of Riemannian Geometry, with a detailed treatment of homogeneous and symmetric spaces, as well as the foundations of the General Theory of Relativity. Starting with the basics of manifolds, it presents key objects of differential geometry, such as Lie groups, vector bundles, and de Rham cohomology, with full mathematical details. Next, the fundamental concepts of Riemannian geometry are introduced, paving the way for the study of homogeneous and symmetric spaces. As an early application, a version of the Poincaré-Hopf and Chern-Gauss-Bonnet Theorems is derived. The final chapter provides an axiomatic deduction of the fundamental equations of the General Theory of Relativity as another important application. Throughout, the theory is illustrated with color figures to promote intuitive understanding, and over 200 exercises are provided (many with solutions) to help master the material. The book is designed to cover a two-semester graduate course for students in mathematics or theoretical physics and can also be used for advanced undergraduate courses. It assumes a solid understanding of multivariable calculus and linear algebra.
650 0 $a Geometry, Differential. $3 523835
650 0 $a Homogeneous spaces. $3 708563
650 1 4 $a Differential Geometry. $3 891003
650 2 4 $a Topological Groups and Lie Groups. $3 3593340
650 2 4 $a Mathematical Physics. $3 1542352
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Universitext. $3 812115
856 4 0 $u https://doi.org/10.1007/978-3-662-69721-4
950 $a Mathematics and Statistics (SpringerNature-11649)