幾何学コロキウム HORO-TIGHT SPHERES IN HYPERBOLIC SPACE

開催日時
2009年   06月 19日 16時 30分 ~ 2009年   06月 19日 18時 00分
場所
北大理学部3号館307室
講演者
泉屋周一(北大)
 
Recently we discovered a new geometry on submanifolds in hyperbolic n-spacewhich is called "Horospherical geometry". This geometry is not invariant underthe hyperbolic motions (it is invariant under the canonical action of SO(n)),but the flatness in this geometry is a hyperbolic invariant. Moreover, the Gauss-Bonnet typetheorem and the Chern-Lashof type theorem for the horospherical curvature hold. In this talk we consider horo-tight immersions of manifolds into hyperbolic n-spaceand give several characterizations of horo-tightness of spheres. As a consequence, we givea complete answer to the following question proposed by T. Cecil and P. Ryan (1985): What are the horo-tight immersions of spheres?

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