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Tubes, Second Edition

Alfred Gray
Book information

Publisher: Birkhäuser Verlag (Basel, Switzerland)
Copyright year: 2004
ISBN: 3764369078
Medium: Hardcover
Pages: 280
Out of print?: N
Additional cataloguing information: Volume 221 of Progress in Mathematics (eds. H. Bass, J. Oesterlé, and A. Weinstein)
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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

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.

*Mathematics > Calculus and Analysis > Differential Geometry
*Mathematics > Geometry > Computational Geometry
*Mathematics > Geometry > Surfaces

Almost complex tructure, Bianchi identity, Bishop-Gunther Inequalities, Cauchy-Schwarz Inequality, Chern class, Chern form, Chern number, complex hypersurface, complex projective space, curvature tensor, double form, Euler characteristic, Fermi coordinates, Gauss equation, Gauss lemma, Gauss-Bonnet integrand, Gauss-Bonnet theorem, holomorphic sectional curvature, Jacobi vector field, Kahler manifold, Kahler submanifold, mean curvature, minimal variety, Myers' theorem, Nash Embedding Theorem, principal curvature, quaternionic projective space, Riccati differential equation, Ricci curvature, scalar curvature, symmetric space, Weingarten map, Weyl tube formula, Wirtinger's inequality