Tubes presents a comprehensive examination of Weyl's tube volume formula, its roots, and its implications. It includes a careful and thorough discussion of each step in the derivation and its application to the Gauss-Bonnet formula. This second edition includes added historical notes and figures in Mathematica.
Graduate students with a basic knowledge of differential geometry will benefit from this text, as will researchers and instructors in analysis, differential geometry, topology, and mathematical physics. Contents
An Introduction to Weyl's Tube Formula | Fermi Coordinates and Fermi Fields | The Riccati Equation for Second Fundamental Forms | The Proof of Weyl's Tube Formula | The Generalized Gauss-Bonnet Theorem | Chern Forms and Chern Numbers | The Tube Formula in the Complex Case | Comparison Theorems for Tube Volumes | Power Series Expansions for Tube Volumes | Steiner's Formula | Mean-value Theorems | Appendices Related Topics
Differential Equations, Geometry