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Introduction to differential geometry

Robbin, Joel W.

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Introduction to differential geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to differential geometry/ by Joel W. Robbin, Dietmar A. Salamon.
Author:	Robbin, Joel W.
other author:	Salamon, D.
Published:	Berlin, Heidelberg :Springer Berlin Heidelberg : : 2022.,
Description:	xiii, 418 p. :ill., digital ;24 cm.
[NT 15003449]:	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
Subject:	Geometry, Differential. -
Online resource:	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
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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.
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