Tubes by Alfred Gray (PDF)

Description

1 An Introduction to Weyl’s Tube Formula.- 3 The Riccati Equation for Second Fundamental Forms.- 4 The Proof of Weyl’s Tube Formula.- 5 The Generalized Gauss-Bonnet Theorem.- 6 Chern Forms and Chern Numbers.- 7 The Tube Formula in the Complex Case.- 8 Comparison Theorems for Tube Volumes.- 9 Power Series Expansions for Tube Volumes.- 10 Steiner’s Formula.- 11 Mean-value Theorems.- Appendix A.- A.2 Moments.- A.3 Computation of the Volume of a Geodesic Ball.- Appendix B.- Notation Index.- Name Index.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The late Alfred Gray had a unique approach to differential geometry. The idea of thickening a geometric object in an ambient space might appear a bit old fashioned as it is not intrinsic, but it gives some elegant approaches to problems in geometry. I could no more find this book in the library. Glad I could still get a used copy.

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