Generalized Curvatures Paperback / softback
by Jean-Marie Morvan
Part of the Geometry and Computing series
Paperback / softback
Description
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.
Information
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Out of stock
- Format:Paperback / softback
- Pages:266 pages, 36 Illustrations, color; 71 Illustrations, black and white; XI, 266 p. 107 illus., 36 ill
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:28/10/2010
- Category:
- ISBN:9783642093005
Other Formats
- Hardback from £81.69
- PDF from £93.08
Information
-
Out of stock
- Format:Paperback / softback
- Pages:266 pages, 36 Illustrations, color; 71 Illustrations, black and white; XI, 266 p. 107 illus., 36 ill
- Publisher:Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication Date:28/10/2010
- Category:
- ISBN:9783642093005
