The horospherical Gauss-Bonnet type theorem in hyperbolic space

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概要

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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.

• 社団法人 日本数学会の論文
• 2006-10-01

著者

• IZUMIYA Shyuichi

  Department of Mathematics Hokkaido University

• Izumiya Shyuichi

  Department Of Mathematics Faculty Of Science Hokkaido University

• Romero Fuster

  Departament De Geometria I Topologia Universitat De Valencia

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