Introduction to Differential Geometry (Paperback, 1st ed. 2022)

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.

General

Imprint:	Springer Spektrum
Country of origin:	Germany
Series:	Springer Studium Mathematik (Master)
Release date:	2022
First published:	2022
Authors:	Joel W Robbin • Dietmar A Salamon
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	418
Edition:	1st ed. 2022
ISBN-13:	978-3-662-64339-6
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Promotions
LSN:	3-662-64339-1
Barcode:	9783662643396

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