Topic
Horosphere
About: Horosphere is a research topic. Over the lifetime, 112 publications have been published within this topic receiving 1320 citations.
Papers published on a yearly basis
Papers
1 Jan 2007
TL;DR: The condition for the curvature of a statistical manifold to admit a kind of standard hypersurface is given in this article as a first step of the statistical submanifold theory.
Abstract: The condition for the curvature of a statistical manifold
to admit a kind of standard hypersurface is given
as a first step of the statistical submanifold theory.
A complex version of the notion of statistical structures
is also introduced.
95 citations
TL;DR: It is shown that the real hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians SU"2","m/S(U"[email protected]?U"m), m>=2.
88 citations
20 Mar 2007
TL;DR: In this paper, a new geometry on submanifolds in hyperbolic $n$-space called horospherical flat surfaces is introduced, which is not invariant under the hyper-bolic motions (it is invariance under the canonical action of $SO(n)$), but it has quite interesting geometric properties.
Abstract: Recently we discovered a new geometry on submanifolds in
hyperbolic $n$-space
which is called {\it horospherical geometry}
Unfortunately this geometry is not invariant under the hyperbolic motions (it is invariant under the canonical action of $SO(n)$), but it has quite interesting
features
For example, the flatness in this geometry is a hyperbolic invariant and the total curvatures are topological invariants In this paper, we investigate the {\it horospherical flat surfaces}
(flat surfaces in the sense of horospherical geometry) in hyperbolic $3$-space
Especially, we give a generic classification of singularities
of such surfaces As a consequence, we can say that such a class of surfaces has
quite a rich geometric structure
70 citations
Posted Content•
TL;DR: In this article, it was shown that the horosphere is the only simply connected annular example, and the catenoid cousins the only annular examples of this nature, and that each annular end of such a surface is asymptotic to an end of a horosphere or a Catenoid.
Abstract: In this paper we shall establish that properly embedded constant mean curvature one surfaces in H^3 of finite topology are of finite total curvature and each end is regular. In particular, this implies the horosphere is the only simply connected such example, and the catenoid cousins the only annular examples of this nature. In general each annular end of such a surface is asymptotic to an end of a horosphere or an end of a catenoid cousin.
66 citations
TL;DR: In this paper, the authors investigated the horospherical flat surfaces (flat surfaces in the sense of horospheric geometry) in hyperbolic 3-space and gave a generic classification of singularities of such surfaces.
Abstract: Recently we discovered a new geometry on submanifolds in hyperbolic n-space which is called horospherical geometry. Unfortunately this geometry is not invariant under the hyperbolic motions (it is invariant under the canonical action of SO(n)), but it has quite interesting features. For example, the flatness in this geometry is a hyperbolic invariant and the total curvatures are topological invariants. In this paper, we investigate the horospherical flat surfaces (flat surfaces in the sense of horospherical geometry) in hyperbolic 3-space. Especially, we give a generic classification of singularities of such surfaces. As a consequence, we can say that such a class of surfaces has quite a rich geometric structure.
63 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 4 |
| 2019 | 6 |
| 2018 | 6 |
| 2017 | 4 |
| 2016 | 12 |