A half-space property for hypersurfaces in the hyperbolic space

被引：0
|
作者：
Velasquez, Marco a. l. [1 ]
机构：
[1] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, PB, Brazil
来源：
ANNALES POLONICI MATHEMATICI | 2024年 / 132卷 / 03期
关键词：
hyperbolic space; complete noncompact hypersurfaces; converge to zero at infinity; hyperspheres; CURVATURE;
D O I：
10.4064/ap230629-31-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Through the study of geometry of the hyperspheres (also known as equidistant spheres) of the hyperbolic space IHIn+1, we establish a nonexistence result for complete noncompact hypersurfaces immersed into IHIn+1 and a characterization of complete totally geodesic hypersurfaces of IHIn+1; namely, we characterize those complete hyperspheres of IHIn+1 with the following geometric property: any geodesic contained in a complete hypersurface is also a geodesic of IHIn+1. Our approach is based on a suitable maximum principle at infinity for complete Riemannian manifolds.
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页数：12
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