Geometry and Computing

# Generalized Curvatures

Authors: Morvan, Jean-Marie

• First coherent and complete account of this subject in book form

eBook $119.00 price for USA (gross) valid through March 31, 2018 • ISBN 978-3-540-73792-6 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Hardcover$159.00
price for USA
valid through March 31, 2018
• ISBN 978-3-540-73791-9
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.
Softcover $159.00 price for USA • ISBN 978-3-642-09300-5 • Free shipping for individuals worldwide • Usually dispatched within 3 to 5 business days. About this book The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space (E ,), endowed with its standard scalar product. Let us state precisely what we mean by a geometric quantity. Consider a subset N S of points of the N-dimensional Euclidean space E , endowed with its standard N scalar product. LetG be the group of rigid motions of E . We say that a 0 quantity Q(S) associated toS is geometric with respect toG if the corresponding 0 quantity Q[g(S)] associated to g(S) equals Q(S), for all g?G . For instance, the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG . But the distance from the origin O to the closest point ofS is not, 0 since it is not invariant under translations ofS. It is important to point out that the property of being geometric depends on the chosen group. For instance, ifG is the 1 N group of projective transformations of E , then the property ofS being a circle is geometric forG but not forG , while the property of being a conic or a straight 0 1 line is geometric for bothG andG . This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on it. Reviews From the reviews: "This book is a welcome addition to the literature in differential geometry. The main aim of this book is the measure of geometric quantities describing a subset of the Euclidean space … endowed with its standard scalar product. … The book contains 107 figures and the bibliography contains about 89 entries. The book covers an active, interesting and fresh research area. It is very useful for researchers in differential geometry and related subjects." (Kazim Ilarslan, Zentralblatt MATH, Vol. 1149, 2008) ## Table of contents (27 chapters) • Introduction Pages 1-10$29.95
• Motivation: Curves

Pages 13-28

$29.95 • Motivation: Surfaces Pages 29-44$29.95
• Distance and Projection

Pages 47-56

$29.95 • Elements of Measure Theory Pages 57-68$29.95

eBook $119.00 price for USA (gross) valid through March 31, 2018 • ISBN 978-3-540-73792-6 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Hardcover$159.00
price for USA
valid through March 31, 2018
• ISBN 978-3-540-73791-9
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.
Softcover \$159.00
price for USA
• ISBN 978-3-642-09300-5
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.

## Bibliographic Information

Bibliographic Information
Book Title
Generalized Curvatures
Authors
Series Title
Geometry and Computing
Series Volume
2
2008
Publisher
Springer-Verlag Berlin Heidelberg
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-73792-6
DOI
10.1007/978-3-540-73792-6
Hardcover ISBN
978-3-540-73791-9
Softcover ISBN
978-3-642-09300-5
Series ISSN
1866-6795
Edition Number
1
Number of Pages
XI, 266
Number of Illustrations and Tables
71 b/w illustrations, 36 illustrations in colour
Topics