Verkauf durch Sack Fachmedien

Morvan

Generalized Curvatures

Medium: Buch
ISBN: 978-3-642-09300-5
Verlag: Springer
Erscheinungstermin: 28.10.2010
Lieferfrist: bis zu 10 Tage

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.


Produkteigenschaften


  • Artikelnummer: 9783642093005
  • Medium: Buch
  • ISBN: 978-3-642-09300-5
  • Verlag: Springer
  • Erscheinungstermin: 28.10.2010
  • Sprache(n): Englisch
  • Auflage: 1. Auflage. Softcover version of original hardcover Auflage 2008
  • Serie: Geometry and Computing
  • Produktform: Kartoniert, Previously published in hardcover
  • Gewicht: 429 g
  • Seiten: 266
  • Format (B x H x T): 155 x 235 x 16 mm
  • Ausgabetyp: Kein, Unbekannt
Autoren/Hrsg.

Autoren

Motivations.- Motivation: Curves.- Motivation: Surfaces.- Background: Metrics and Measures.- Distance and Projection.- Elements of Measure Theory.- Background: Polyhedra and Convex Subsets.- Polyhedra.- Convex Subsets.- Background: Classical Tools in Differential Geometry.- Differential Forms and Densities on EN.- Measures on Manifolds.- Background on Riemannian Geometry.- Riemannian Submanifolds.- Currents.- On Volume.- Approximation of the Volume.- Approximation of the Length of Curves.- Approximation of the Area of Surfaces.- The Steiner Formula.- The Steiner Formula for Convex Subsets.- Tubes Formula.- Subsets of Positive Reach.- The Theory of Normal Cycles.- Invariant Forms.- The Normal Cycle.- Curvature Measures of Geometric Sets.- Second Fundamental Measure.- Applications to Curves and Surfaces.- Curvature Measures in E2.- Curvature Measures in E3.- Approximation of the Curvature of Curves.- Approximation of the Curvatures of Surfaces.- On Restricted Delaunay Triangulations.