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＜電子ブック＞
Introduction to Differential Geometry / by Joel W. Robbin, Dietmar A. Salamon
(Springer Studium Mathematik. ISSN:25099329)

版	1st ed. 2022.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Spektrum)
出版年	2022
大きさ	XIII, 418 p. 45 illus. in color : online resource
著者標目	*Robbin, Joel W author Salamon, Dietmar A author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential FREE:Differential Geometry
一般注記	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 Zürich (ETHZ), Departement Mathematik HTTP:URL=https://doi.org/10.1007/978-3-662-64340-2

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