Dept. Math, Hokkaido Univ. EPrints Server

Horo-tight spheres in Hyperbolic space

Preprint Series # 932
Buosi, Marcelo and Izumiya, Shyuichi and Maria Aparecida, Soares Ruas Horo-tight spheres in Hyperbolic space. (14 January 2009); (Submitted)

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We study horo-tight immersions of manifolds into hyperbolic spaces. The main result gives several characterizations of horo-tightness of spheres, answering a question proposed by T. Cecil and P. Ryan. For instance, we prove that a sphere is horo-tight if and only if it is tight in the hyperbolic sense. For codimension bigger than one, it follows that horo-tight spheres in hyperbolic space are metric spheres. We also prove that horo-tight hyperspheres are characterized by the property that both of its total absolute horospherical curvatures attend their minimum value. We also introduce the notion of weak horo-tightness: an immersion is weak horo-tight if only one of its total absolute curvature attends its minimum. We prove a characterization theorem for weak horo-tight hyperspheres.

Item Type:Preprint
Uncontrolled Keywords:Horospherical Geometry, Horo-tight immersion
ID Code:1976