Slant geometry of spacelike hypersurfaces in hyperbolic space and de Sitter space

被引：9

作者：

Asayama, Mikuri ^{[1
]}

Izumiya, Shyuichi ^{[1
]}

Tamaoki, Aiko ^{[1
]}

Yildirim, Handan ^{[2
]}

机构：

[1] Hokkaido Univ, Dept Math, Sapporo, Hokkaido 0600810, Japan

[2] Istanbul Univ, Dept Math, Fac Sci, TR-34134 Istanbul, Turkey

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2012年 / 28卷 / 02期

关键词：

Legendrian dualities; spacelike hypersurfaces; hyperbolic space; de Sitter space; Lorentz-Minkowski space; LEGENDRIAN DUALITIES; HOROSPHERICAL GEOMETRY; PSEUDO-SPHERES; SUBMANIFOLDS; LIGHTCONE; MANDALA;

D O I：

10.4171/RMI/681

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a one-parameter family of new extrinsic differential geometries on hypersurfaces in hyperbolic space. Recently, the second author and his collaborators have constructed a new geometry which is called horospherical geometry on hyperbolic space. There is another geometry which is the famous Gauss-Bolyai-Robecheyski geometry (i.e., the hyperbolic geometry) on hyperbolic space. The slant geometry is a one-parameter family of geometries which connect these two geometries. Moreover, we construct a one-parameter family of geometries on spacelike hypersurfaces in de Sitter space.

引用

页码：371 / 400

页数：30

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