Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space

Weiller F. C. Barboza; H. F. de Lima; M. A. Velásquez

Commentationes Mathematicae Universitatis Carolinae (2023)

  • Volume: 64, Issue: 1, page 39-61
  • ISSN: 0010-2628

Abstract

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In this paper, we deal with n -dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space L p n + p of index p > 1 , which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric to an isoparametric submanifold of the ambient space. For this, we use three main core analytical tools: a suitable version of the Omori–Yau maximum principle, parabolicity with respect to a modified Cheng–Yau operator and a certain integrability property.

How to cite

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Barboza, Weiller F. C., de Lima, H. F., and Velásquez, M. A.. "Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space." Commentationes Mathematicae Universitatis Carolinae 64.1 (2023): 39-61. <http://eudml.org/doc/299333>.

@article{Barboza2023,
abstract = {In this paper, we deal with $n$-dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space $L_\{p\}^\{n+p\}$ of index $p>1$, which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric to an isoparametric submanifold of the ambient space. For this, we use three main core analytical tools: a suitable version of the Omori–Yau maximum principle, parabolicity with respect to a modified Cheng–Yau operator and a certain integrability property.},
author = {Barboza, Weiller F. C., de Lima, H. F., Velásquez, M. A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally symmetric semi-Riemannian space; mean curvature vector field; complete linear Weingarten spacelike submanifold; totally umbilical submanifold; isoparametric submanifold; $\mathcal \{L\}$-parabolicity},
language = {eng},
number = {1},
pages = {39-61},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space},
url = {http://eudml.org/doc/299333},
volume = {64},
year = {2023},
}

TY - JOUR
AU - Barboza, Weiller F. C.
AU - de Lima, H. F.
AU - Velásquez, M. A.
TI - Revisiting linear Weingarten spacelike submanifolds immersed in a locally symmetric semi-Riemannian space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 1
SP - 39
EP - 61
AB - In this paper, we deal with $n$-dimensional complete linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector field and flat normal bundle in a locally symmetric semi-Riemannian space $L_{p}^{n+p}$ of index $p>1$, which obeys some curvature constraints (such an ambient space can be regarded as an extension of a semi-Riemannian space form). Under appropriate hypothesis, we are able to prove that such a spacelike submanifold is either totally umbilical or isometric to an isoparametric submanifold of the ambient space. For this, we use three main core analytical tools: a suitable version of the Omori–Yau maximum principle, parabolicity with respect to a modified Cheng–Yau operator and a certain integrability property.
LA - eng
KW - locally symmetric semi-Riemannian space; mean curvature vector field; complete linear Weingarten spacelike submanifold; totally umbilical submanifold; isoparametric submanifold; $\mathcal {L}$-parabolicity
UR - http://eudml.org/doc/299333
ER -

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