Integral geometry of equidistants in hyperbolic space

Gil Solanes*

*Autor corresponent d’aquest treball

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Resum

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. Analogous formulas are given for totally umbilical hypersurfaces contained in totally geodesic planes of ℍn.

Idioma originalEnglish
Pàgines (de-a)271-284
Nombre de pàgines14
RevistaIsrael Journal of Mathematics
Volum145
DOIs
Estat de la publicacióPublicada - 2005

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