Spacelike foliations on Lorentz manifolds

被引：0
作者：
Brasil, Aldir [1 ]
Deshmukh, Sharief [2 ]
da Silva, Euripedes [3 ]
Sousa, Paulo [4 ]
机构：
[1] Univ Fed Ceara, Campus Pici, BR-60455760 Fortaleza, Ceara, Brazil
[2] King Saud Univ, Riyadh 11451, Saudi Arabia
[3] Inst Fed Educ Ciencia & Tecnol Ceara, Ave Parque Cent 1315, BR-61939140 Maracanau, Ceara, Brazil
[4] Univ Fed Piaui, BR-64049550 Teresina, Piaui, Brazil
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2025年 / 99卷
关键词：
Foliations; Totally umbilic; Stable hypersurface; Totally geodesic; CONSTANT MEAN-CURVATURE; HYPERSURFACES; STABILITY;
D O I：
10.1016/j.difgeo.2025.102235
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We investigate conditions for the leaves being stable, totally geodesic or totally umbilical. We consider that Mn+1 is equipped with a timelike closed conformal vector field xi. If the foliation has constant mean curvature, we show that the leaves are stable. When the leaves are compact spacelike hypersurfaces we show that, under certain conditions, its are totally umbilic hypersurfaces. In the case of foliations by complete noncompact hypersurfaces, we using a Maximum Principle at infinity to conclude that the foliation is totally geodesic. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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页数：12
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