Complete hypersurfaces with two distinct principal curvatures in a locally symmetric Riemannian manifold

被引：6

作者：

Gomes, Jose N. ^{[1
]}

de Lima, Henrique F. ^{[2
]}

dos Santos, Fabio R. ^{[2
]}

Velasquez, Marco Antonio L. ^{[2
]}

机构：

[1] Univ Fed Amazonas, Dept Matemat, BR-69077070 Manaus, Amazonas, Brazil

[2] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 133卷

关键词：

Locally symmetric Riemannian manifolds; Hypersurfaces with two distinct principal curvatures; Complete linear Weingarten hypersurfaces; Isoparametric hypersurfaces; LINEAR WEINGARTEN HYPERSURFACES; CONSTANT MEAN-CURVATURE; MINIMAL HYPERSURFACES; SPACE-FORMS; RIGIDITY; SPHERE;

D O I：

10.1016/j.na.2015.11.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal with complete hypersurfaces with two distinct principal curvatures in a locally symmetric Riemannian manifold, which is supposed to obey some appropriated curvature constraints. Initially, considering the case that such a hypersurface has constant mean curvature, we apply a Simons type formula jointly with the well known generalized maximum principle of Omori-Yau to show that it must be isometric to an isoparametric hypersurface of the ambient space. Afterwards, we use a Cheng-Yau modified operator in order to obtain a sort of extension of this previously mentioned result for the context of linear Weingarten hypersurfaces, that is, hypersurfaces whose mean and scalar curvatures are linearly related. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：15 / 27

页数：13

共 40 条

[1] On the complete spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space
de Lima, Henrique F.
dos Santos, Fabio R.
Gomes, Jose N.
Velasquez, Marco Antonio L.
COLLECTANEA MATHEMATICA, 2016, 67 (03) : 379 - 397
[2] CHARACTERIZATIONS OF COMPLETE HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLDS
Araujo, Jogli G.
Batista, Marcio
De Lima, Henrique F.
COLLOQUIUM MATHEMATICUM, 2018, 153 (02) : 149 - 162
[3] Complete Hypersurfaces with Two Distinct Principal Curvatures in a Space Form
Gomes, Jose N.
de Lima, Henrique F.
Velasquez, Marco Antonio L.
RESULTS IN MATHEMATICS, 2015, 67 (3-4) : 457 - 470
[4] On the complete spacelike hypersurfaces immersed with two distinct principal curvatures in a locally symmetric Lorentz space
Henrique F. de Lima
Fábio R. dos Santos
José N. Gomes
Marco Antonio L. Velásquez
Collectanea Mathematica, 2016, 67 : 379 - 397
[5] Complete Hypersurfaces with Two Distinct Principal Curvatures in a Space Form
José N. Gomes
Henrique F. de. Lima
Marco Antonio L. Velásquez
Results in Mathematics, 2015, 67 : 457 - 470
[6] A MAXIMUM PRINCIPLE FOR COMPLETE HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLD
Zhang, Shicheng
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 29 (01): : 141 - 153
[7] On complete linear Weingarten hypersurfaces in locally symmetric Riemannian manifolds
Aquino, Cicero P.
de Lima, Henrique F.
dos Santos, Fabio R.
Velasquez, Marco Antonio L.
COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2015, 56 (04): : 515 - 529
[8] RIGIDITY THEOREMS OF HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLD
Zhang, Shicheng
Wu, Baoqiang
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 141 (11) : 4015 - 4025
[9] Revisiting linear Weingarten hypersurfaces immersed into a locally symmetric Riemannian manifold
Eudes L. de Lima
Henrique F. de Lima
Lucas S. Rocha
European Journal of Mathematics, 2022, 8 : 388 - 402
[10] Revisiting linear Weingarten hypersurfaces immersed into a locally symmetric Riemannian manifold
de Lima, Eudes L.
de Lima, Henrique F.
Rocha, Lucas S.
EUROPEAN JOURNAL OF MATHEMATICS, 2022, 8 (01) : 388 - 402

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