CORRESPONDENCES OF HYPERSURFACES IN HYPERBOLIC POINCARE MANIFOLDS AND CONFORMALLY INVARIANT PDES

被引：5

作者：

Bonini, Vincent ^{[1
]}

Espinar, Jose M. ^{[2
]}

Qing, Jie ^{[3
]}

机构：

[1] Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93407 USA

[2] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

[3] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2010年 / 138卷 / 11期

关键词：

Hyperbolic Poincare manifold; hypersurfaces; second fundamental form; Schouten tensor; conformally invariant PDE; CURVATURE; EQUATIONS; METRICS;

D O I：

10.1090/S0002-9939-2010-10512-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

On a hyperbolic Poincare manifold, we derive an explicit relationship between the eigenvalues of Weyl-Schouten tensor of a conformal representative of the conformal infinity and the principal curvatures of the level sets of the associated geodesic defining function. This considerably simplifies the arguments and generalizes the results of Galvez, Mira and the second author. In particular, we obtain the equivalence between Christoffel-type problems for hypersurfaces in a hyperbolic Poincare manifold and scalar curvature problems on the conformal infinity.

引用

页码：4109 / 4117

页数：9

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