具有积分条件的时空中的广义Alexandrov定理

IF 0.7 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2025-05-14 DOI:10.1016/j.difgeo.2025.102254

Kwok-Kun Kwong , Xianfeng Wang

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引用次数: 0

摘要

我们研究了涉及平均曲率向量H→或混合高阶平均曲率的积分条件，以确定一个协维二子流形Σ何时位于时空中无剪切（脐带）零超曲面上。我们通过放宽Σ上的曲率条件，从几个方面推广了[18]中引入的时空中的alexandrov型定理。具体地说，我们用平均曲率积分不等式给出了Σ位于无剪切零超曲面的充分必要条件。我们方法的一个关键组成部分是使用具有任意权值的闵可夫斯基公式，它使我们能够推导出具有明显较弱积分曲率条件的子流形的刚度结果。

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Generalized Alexandrov theorems in spacetimes with integral conditions

We investigate integral conditions involving the mean curvature vector

\vec{H}

or mixed higher-order mean curvatures, to determine when a codimension-two submanifold Σ lies on a shear-free (umbilical) null hypersurface in a spacetime. We generalize the Alexandrov-type theorems in spacetime introduced in [18] by relaxing the curvature conditions on Σ in several aspects. Specifically, we provide a necessary and sufficient condition, in terms of a mean curvature integral inequality, for Σ to lie in a shear-free null hypersurface. A key component of our approach is the use of Minkowski formulas with arbitrary weight, which enables us to derive rigidity results for submanifolds with significantly weaker integral curvature conditions.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.