Tubes
(Sprache: Englisch)
This book expresses the full understanding of Weyl's formula for the volume of a tube, its roots and its implications. Historical notes and Mathematica drawings have been added to this revised second edition.
From the reviews:
"Will do much to make Weyl's...
From the reviews:
"Will do much to make Weyl's...
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Klappentext zu „Tubes “
This book expresses the full understanding of Weyl's formula for the volume of a tube, its roots and its implications. Historical notes and Mathematica drawings have been added to this revised second edition.From the reviews:
"Will do much to make Weyl's tube formula more accessible to modern readers.... A high point is the presentation of estimates for the volumes of tubes in ambient Riemannian manifolds whose curvature is bounded above or below."
--BULLETIN OF THE AMS
Inhaltsverzeichnis zu „Tubes “
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.
Bibliographische Angaben
- Autor: Alfred Gray
- 2nd ed. 2004, 300 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer Basel
- ISBN-10: 3764369078
- ISBN-13: 9783764369071
- Erscheinungsdatum: 27.11.2003
Sprache:
Englisch
Rezension zu „Tubes “
"The new book by Alfred Gray will do much to make Weyl's tube formula more accessible to modern readers. The first five chapters give a careful and thorough discussion of each step in the derivation and its application to the Gauss-Bonnet formula. Gray's pace is quite leisurely, and a gradualte student who has completed a basic differential geometry course will have little difficulty following the presentation.
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