








Tubes, Second Edition












Publisher:  Birkhäuser Verlag (Basel, Switzerland) 
Additional cataloguing information:  Volume 221 of Progress in Mathematics (eds. H. Bass, J. Oesterlé, and A. Weinstein) 
  






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 GaussBonnet 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  Meanvalue 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 GaussBonnet 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.












Almost complex tructure, Bianchi identity, BishopGunther Inequalities, CauchySchwarz Inequality, Chern class, Chern form, Chern number, complex hypersurface, complex projective space, curvature tensor, double form, Euler characteristic, Fermi coordinates, Gauss equation, Gauss lemma, GaussBonnet integrand, GaussBonnet 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







   
 
