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Total absolute horospherical curvature of submanifolds in hyperbolic space
(WALTER DE GRUYTER & CO, 2010)
We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of M, which implies, for the horospherical geometry, the analogues of ...
Horo-tight spheres in hyperbolic space
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 Cecil and Ryan. For instance, we prove that ...
The magnetic flow on the manifold of oriented geodesics of a three dimensional space form
(Osaka University. Departments of Mathematics, 2013-09)
Let M be the three dimensional complete simply connected manifold of constant sectional curvature 0,10,1 or −1−1. Let L be the manifold of all (unparametrized) complete oriented geodesics of M, endowed with its canonical ...