東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁 到查詢結果 [ subject:"Differential Geometry." ]

切換: 標籤 | MARC模式 | ISBD

Introduction to differential geometry

Robbin, Joel W.

FindBook

Google Book

Amazon

博客來

Introduction to differential geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Introduction to differential geometry/ by Joel W. Robbin, Dietmar A. Salamon.
作者:	Robbin, Joel W.
其他作者:	Salamon, D.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2022.,
面頁冊數:	xiii, 418 p. :ill., digital ;24 cm.
內容註:	1 What is Differential Geometry? -- 2 Foundations -- 3 The Levi-Civita Connection -- 4 Geodesics -- 5 Curvature -- 6 Geometry and Topology -- 7 Topics in Geometry -- Appendix.
Contained By:	Springer Nature eBook
標題:	Geometry, Differential. -
電子資源:	https://doi.org/10.1007/978-3-662-64340-2
ISBN:	9783662643402

Introduction to differential geometry
Robbin, Joel W.

Introduction to differential geometry[electronic resource] /by Joel W. Robbin, Dietmar A. Salamon. - Berlin, Heidelberg :Springer Berlin Heidelberg :2022. - xiii, 418 p. :ill., digital ;24 cm. - Springer studium mathematik (master). - Springer studium mathematik.Master..

1 What is Differential Geometry? -- 2 Foundations -- 3 The Levi-Civita Connection -- 4 Geodesics -- 5 Curvature -- 6 Geometry and Topology -- 7 Topics in Geometry -- Appendix.

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. The Authors Joel W. Robbin, Professor emeritus, University of Wisconsin-Madison, Department of Mathematics. Dietmar A. Salamon, Professor emeritus, Eidgenössische Technische Hochschule Zurich (ETHZ), Departement Mathematik.

ISBN: 9783662643402

Standard No.: 10.1007/978-3-662-64340-2doiSubjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA641 / .R63 2022

Dewey Class. No.: 516.36

Introduction to differential geometry
LDR:02658nmm a2200337 a 4500 001 2297564
003 DE-He213
005 20220113195518.0
006 m d
007 cr nn 008maaau
008 230324s2022 gw s 0 eng d
020 $a 9783662643402 $q (electronic bk.)
020 $a 9783662643396 $q (paper)
024 7 $a 10.1007/978-3-662-64340-2 $2 doi
035 $a 978-3-662-64340-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA641 $b .R63 2022
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 .R631 2022
100 1 $a Robbin, Joel W. $3 658901
245 1 0 $a Introduction to differential geometry $h [electronic resource] / $c by Joel W. Robbin, Dietmar A. Salamon.
260 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer Spektrum, $c 2022.
300 $a xiii, 418 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer studium mathematik (master)
505 0 $a 1 What is Differential Geometry? -- 2 Foundations -- 3 The Levi-Civita Connection -- 4 Geodesics -- 5 Curvature -- 6 Geometry and Topology -- 7 Topics in Geometry -- Appendix.
520 $a 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. The Authors Joel W. Robbin, Professor emeritus, University of Wisconsin-Madison, Department of Mathematics. Dietmar A. Salamon, Professor emeritus, Eidgenössische Technische Hochschule Zurich (ETHZ), Departement Mathematik.
650 0 $a Geometry, Differential. $3 523835
650 1 4 $a Differential Geometry. $3 891003
700 1 $a Salamon, D. $q (Dietmar) $3 2047734
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Springer studium mathematik. $p Master. $3 3593348
856 4 0 $u https://doi.org/10.1007/978-3-662-64340-2
950 $a Mathematics and Statistics (SpringerNature-11649)