Tubes - Hardcover

Gray, Alfred

Hardcover

ISBN 10: 0201156768 ISBN 13: 9780201156768

Publisher: Addison Wesley Longman Publishing Co, 1990

Synopsis

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

About this title

Review

"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)

Edition details

• Publisher: Addison Wesley Longman Publishing Co
• Publication date: 1990
• Language: English
• ISBN 10: 0201156768
• ISBN 13: 9780201156768
• Binding: Hardcover
• Number of pages: 283