Tubes : Progress In Mathematics - Alfred Gray

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Tubes

By: Alfred Gray

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Hardcover | 27 November 2003 | Edition Number 2

At a Glance

Hardcover
300 Pages

Edition Type
Revised

Dimensions(cm)
23.5 x 15.88 x 1.91

Hardcover

$169.00

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In July 1998, I received an e-mail from Alfred Gray, telling me: " . . . I am in Bilbao and working on the second edition of Tubes . . . Tentatively, the new features of the book are: 1. Footnotes containing biographical information and portraits 2. A new chapter on mean-value theorems 3. A new appendix on plotting tubes " That September he spent a week in Valencia, participating in a workshop on Differential Geometry and its Applications. Here he gave me a copy of the last version of Tubes. It could be considered a final version. There was only one point that we thought needed to be considered again, namely the possible completion of the material in Section 8. 8 on comparison theorems of surfaces with the now well-known results in arbitrary dimensions. But only one month later the sad and shocking news arrived from Bilbao: Alfred had passed away. I was subsequently charged with the task of preparing the final revision of the book for the publishers, although some special circumstances prevented me from finishing the task earlier. The book appears essentially as Alred Gray left it in September 1998. The only changes I carried out were the addition of Section 8. 9 (representing the discus- sion we had), the inclusion of some new results on harmonic spaces, the structure of Hopf hypersurfaces in complex projective spaces and the conjecture about the volume of geodesic balls.

Industry Reviews

"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)

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You Can Find This Book In

Non-Fiction Mathematics Geometry Differential & Riemannian Geometry

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Non-Fiction Mathematics Geometry Differential & Riemannian Geometry

Preface to the Second Edition
Preface
An Introduction to Weyl's Tube Formula	p. 1
Fermi Coordinates and Fermi Fields	p. 13
The Riccati Equation for Second Fundamental Forms	p. 31
The Proof of Weyl's Tube Formula	p. 53
The Generalized Gauss-Bonnet Theorem	p. 71
Chern Forms and Chern Numbers	p. 85
The Tube Formula in the Complex Case	p. 117
Comparison Theorems for Tube Volumes	p. 143
Power Series Expansions for Tube Volumes	p. 185
Steiner's Formula	p. 209
Mean-value Theorems	p. 231
App. A	p. 247
App. B	p. 255
Index	p. 273
Notation Index	p. 277
Name Index	p. 279
Table of Contents provided by Blackwell. All Rights Reserved.

Tubes

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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