稳态空间中类空间超平面的新性质

IF 0.3 4区数学 Q4 MATHEMATICS

Mathematica Scandinavica Pub Date : 2020-03-29 DOI:10.7146/math.scand.a-117703

C. Aquino, H. Baltazar, H. Lima

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引用次数: 3

摘要

在本文中，我们处理了浸入de Sitter空间Sn+11的开放区域中的完全类空超曲面，该开放区域被称为稳态空间Hn+1。在这些超曲面的高阶平均曲率行为的适当约束下，我们能够证明它们一定是Hn+1的类空间超平面。此外，通过对Hn+1的双曲柱面的分析，我们讨论了主要假设在我们的结果中的重要性。我们的方法是基于完全黎曼流形无穷大的广义极大值原理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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New characterizations of spacelike hyperplanes in the steady state space

In this article, we deal with complete spacelike hypersurfaces immersed in an open region of the de Sitter space Sn+11 which is known as the steady state space Hn+1. Under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we are able to prove that they must be spacelike hyperplanes of Hn+1. Furthermore, through the analysis of the hyperbolic cylinders of Hn+1, we discuss the importance of the main hypothesis in our results. Our approach is based on a generalized maximum principle at infinity for complete Riemannian manifolds.

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.