The Variational Theory of Geodesics

by M. M. Postnikov, Bernard R. Gelbaum (Editor)

Overview

Riemannian geometry is a fundamental area of modern mathematics and is important to the study of relativity. Within the larger context of Riemannian mathematics, the active subdiscipline of geodesics (shortest paths) in Riemannian spaces is of particular significance. This compact and self-contained text by a noted theorist presents the essentials of modern differential geometry as well as basic tools for the study of Morse theory. The advanced treatment emphasizes analytical rather than topological aspects of Morse theory and requires a solid background in calculus.
Suitable for advanced undergraduates and graduate students of mathematics, the text opens with a chapter on smooth manifolds, followed by a consideration of spaces of affine connection. Subsequent chapters explore Riemannian spaces and offer an extensive treatment of the variational properties of geodesics and auxiliary theorems and matters.

Product Details

ISBN-13:	9780486845166
Publisher:	Dover Publications
Publication date:	11/13/2019
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	208
File size:	36 MB
Note:	This product may take a few minutes to download.

About the Author

Soviet mathematician Mikhail Mikhailovich Postnikov (1927–2004) worked primarily in algebraic and differential topology. He was on the Mechanics and Mathematics faculty of Moscow State University.

Table of Contents

Contents: 
1. Smooth Manifolds. 
2. Spaces of Affine Connection. 
3. Riemannian Spaces. 
4. The Variational Properties of Geodesics. 
Appendix to Ch. 4
5. A Reduction Theorem. 
Index.