Approximation of the second fundamental form of a hypersurface of a Riemannian manifold - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports Year : 2003

Approximation of the second fundamental form of a hypersurface of a Riemannian manifold

David Cohen-Steiner
  • Function : Author
  • PersonId : 833472
Jean-Marie Morvan
  • Function : Author

Abstract

We give a general Riemannian framework to the study of approximation of curvature measures, using the theory of the normal cycle. Moreover, we introduce a differential form which allows to define a new type of curvature measure encoding the second fundamental form of a hypersurface, and to extend this notion to geometric compact subsets of a Riemannian manifold . Finally, if a geometric compact subset is close to a smooth hypersurface of a Riemannian manifold, we compare their second fundamental form (in the previous sense), and give a bound of their difference in terms of geometric invariants and the mass of the involved normal cycles.
Fichier principal
Vignette du fichier
RR-4868.pdf (311.73 Ko) Télécharger le fichier

Dates and versions

inria-00071715 , version 1 (23-05-2006)

Identifiers

  • HAL Id : inria-00071715 , version 1

Cite

David Cohen-Steiner, Jean-Marie Morvan. Approximation of the second fundamental form of a hypersurface of a Riemannian manifold. RR-4868, INRIA. 2003. ⟨inria-00071715⟩
104 View
209 Download

Share

Gmail Facebook Twitter LinkedIn More