Totally umbilical hypersurfaces of product spaces

被引：2
|
作者：
de Lima, Ronaldo F. [1 ]
dos Santos, Joao Paulo [2 ]
机构：
[1] Univ Fed Rio Grande do Norte, Dept Matemat, Natal, RN, Brazil
[2] Univ Brasilia, Dept Matemat, Brasilia, DF, Brazil
来源：
MANUSCRIPTA MATHEMATICA | 2022年 / 169卷 / 3-4期
关键词：
MANIFOLDS;
D O I：
10.1007/s00229-021-01339-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a Riemannian manifold M, and an open interval I subset of R, we characterize nontrivial totally umbilical hypersurfaces of the product M x I-as well as of warped products I x(omega) M-as those which are local graphs built on isoparametric families of totally umbilical hypersurfaces of M. By means of this characterization, we fully extend to S-n x R and H-n x R the results by Souam and Toubiana on the classification of totally umbilical surfaces in S-2 x R and H-2 x R. It is also shown that an analogous classification holds for arbitrary warped products I x(omega) S-n and I x(omega) H-n.
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页码：649 / 666
页数：18
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