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Tubes : Progress in Mathematics - Alfred Gray

Tubes

Progress in Mathematics

Hardcover

Published: 27th November 2003
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The main subject of the book is the full understanding of Weyl's formula for the volume of a tube, its roots and its implications. Another discussed approach to the study of volumes of tubes is the computation of the power series of the volume of a tube as a function of its radius. The chapter on mean values, besides its intrinsic interest, shows an interesting fact: methods which are useful for volumes are also useful for problems related with the Laplacian. Historical notes and Mathematica drawings have been added to this revised second edition.

"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.

In the remaining chapters of the book, one can find an extension of Weyl's tube formula to complex submanifolds of complex projective space, power series expansions for tube volumes, and the 'half-tube formula' for hypersurfaces. 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 (Review of the First Edition)

Preface to the Second Edition
Preface
An Introduction to Weyl's Tube Formulap. 1
Fermi Coordinates and Fermi Fieldsp. 13
The Riccati Equation for Second Fundamental Formsp. 31
The Proof of Weyl's Tube Formulap. 53
The Generalized Gauss-Bonnet Theoremp. 71
Chern Forms and Chern Numbersp. 85
The Tube Formula in the Complex Casep. 117
Comparison Theorems for Tube Volumesp. 143
Power Series Expansions for Tube Volumesp. 185
Steiner's Formulap. 209
Mean-value Theoremsp. 231
App. Ap. 247
App. Bp. 255
Indexp. 273
Notation Indexp. 277
Name Indexp. 279
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783764369071
ISBN-10: 3764369078
Series: Progress in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 280
Published: 27th November 2003
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 23.5 x 15.5  x 1.91
Weight (kg): 0.61
Edition Number: 2
Edition Type: Revised