Overview
- Geometric discussion of Weyl's original ideas
- Original approaches to Weyl's volume formula
- Many Mathematica drawings and remarks on 'how to draw a tube'
Part of the book series: Progress in Mathematics (PM, volume 221)
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Table of contents (11 chapters)
Keywords
About this book
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)
Bibliographic Information
Book Title: Tubes
Authors: Alfred Gray
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-7966-8
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 2004
Hardcover ISBN: 978-3-7643-6907-1Published: 27 November 2003
Softcover ISBN: 978-3-0348-9639-9Published: 06 November 2012
eBook ISBN: 978-3-0348-7966-8Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 2
Number of Pages: XIII, 280
Additional Information: Originally published by Addison-Wesley, 1990
Topics: Geometry, Differential Geometry