We'd like to understand how you use our websites in order to improve them. Register your interest. We generalize the classical formulas of integral geometry, by getting integral geometric formulas for the intersection of a fixed compact hypersurface of hyperbolic space and a moving totally umbilical hypersurface. In particular we compute the mean value of the volume, the total mean curvatures and the Euler characteristic of these intersections when the totally umbilical hypersurface moves over all the intersecting positions. This is a preview of subscription content, log in to check access.
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We'd like to understand how you use our websites in order to improve them. Register your interest. Our results generalize the other authors work in three major steps, domain, range and the codimension of immersions.
As a byproduct, we obtain the non-embedding theorems Chern-Kuiper, Moore and Jacobowitz. The proofs are based on the maximum comparison principle. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Borovskii and S. Google Scholar. Burago, V. Cheeger and D. Chern and N. Coghlan and Y. Dajzer, Submanifolds and Isometric Immersions , Math. Fontenele and S. Gilbarg and N.
Hicks, Notes on Differential Geometry , D. Ishihara, Radii of immersed manifolds and non-existence of immersioss , Proc. Jorge and D. Jorge and F. Schoen and S. Yau, Lectures on Differential Geometry , Vol. I, International Press, Dedicata, 68 : , 73— Download references. Ranjbar-Motlagh, A. Rigidity of spheres in Riemannian manifolds and a non-embedding theorem. Mat 32, — Download citation.
Received : 08 November Issue Date : June Search SpringerLink Search. Immediate online access to all issues from Subscription will auto renew annually. References [BS] Yu. You can also search for this author in PubMed Google Scholar. About this article Cite this article Ranjbar-Motlagh, A.
Integral geometry of equidistants in hyperbolic space
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Coleção Projeto Euclides
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Geometria Riemanniana (Em Portuguese do Brasil)