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Introduction to Differential Geometry (Springer Studium Mathematik (Master)) by Joel W. Robbin, Dietmar A. Salamon is a nonfiction available to read on EtoBox.

What is Introduction to Differential Geometry (Springer Studium Mathematik (Master)) about?

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 th

Who reads Introduction to Differential Geometry (Springer Studium Mathematik (Master))?

Author

Joel W. Robbin, Dietmar A. Salamon

Publisher

Springer Spektrum. in Springer-Verlag GmbH

Published

2022

Language

EN

ISBN

9783662643396

Category

nonfiction

Subjects

Mathematics, Geometry And Topology, Stem