We introduce the notion horospherical curvatures of hypersurfaces in hyperbolic space andshow that totally umbilic hypersurfaces with vanishing curvatures are only horospheres. We also show that the Gauss-Bonnet type theorem holds for the horospherical Gauss-Kronecker curvature of a closed orientable even dimensional hypersurface in hyperbolic space.
Publié le : 2006-10-14
Classification:
hyperbolic space,
hypersurfaces,
hyperbolic Gauss maps,
horospherical geometry,
Gauss-Bonnet type theorem,
53A35,
53A05,
58C27
@article{1179759532,
author = {IZUMIYA, Shyuichi and ROMERO FUSTER, Mar\'\i a del Carmen},
title = {The horospherical Gauss-Bonnet type theorem in hyperbolic space},
journal = {J. Math. Soc. Japan},
volume = {58},
number = {3},
year = {2006},
pages = { 965-984},
language = {en},
url = {http://dml.mathdoc.fr/item/1179759532}
}
IZUMIYA, Shyuichi; ROMERO FUSTER, María del Carmen. The horospherical Gauss-Bonnet type theorem in hyperbolic space. J. Math. Soc. Japan, Tome 58 (2006) no. 3, pp. 965-984. http://gdmltest.u-ga.fr/item/1179759532/