The horospherical Gauss-Bonnet type theorem in hyperbolic space
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We introduce the notion horospherical curvatures of hypersurfaces in hyperbolic space and show 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.
- Tokyo Sugaku Kaisya Zasshi
Tokyo Sugaku Kaisya Zasshi 58(4), 965-984, 2006-10-01
The Mathematical Society of Japan