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Introduction to differential geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Introduction to differential geometryby 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.
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$q(electronic bk.)

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$q(electronic bk.)

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

182610
Geometry, Differential.

LC Class. No.: QA641 / .R63 2022

Dewey Class. No.: 516.36

Introduction to differential geometry
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