Integral geometry of equidistants in hyperbolic space

Gil Solanes*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)271-284
Number of pages14
JournalIsrael Journal of Mathematics
Volume145
DOIs
Publication statusPublished - 2005

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