The Variational Theory of Geodesics (Paperback)

Paperback. 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. AUTHOR: Soviet mathematician Mikhail Mikhailovich Postnikov (19272004) worked primarily in algebraic and differential topology. He was on the Mechanics and Mathematics faculty of Moscow State University. Compact, self-contained text by a noted theorist presents essentials of modern differential geometry and basic tools for study of Morse theory. Advanced treatment emphasizes Morse theory's analytical rather than topological aspects. 1967 edition. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. …