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A Characterization of Linear Weingarten Submanifolds in a Semi-Riemannian Space Form with Arbitrary Index
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2020-10-29 , DOI: 10.1007/s00009-020-01641-0
Dan Yang , Yu Fu

In this paper, we deal with the spacelike linear Weingarten submanifolds with parallel normalized mean curvature vector in an \((n+p)\)-dimensional semi-Riemannian space form \(N^{n+p}_{q}(c)\) of constant sectional curvature c with index q, where \(1\le q\le p\). In this setting, we obtain an important inequality and apply some appropriated generalized maximum principles to a suitable Cheng–Yau-modified operator to obtain some characterizations of the linear Weingarten submanifolds.



中文翻译:

具有任意指数的半黎曼空间形式中线性Weingarten子流形的刻画

在本文中,我们以\((n + p)\)维半黎曼空间形式\(N ^ {n + p} _ {q}(处理具有平行归一化平均曲率向量的类空线性Weingarten子流形c)\)的恒定截面曲率c为索引q,其中\(1 \ le q \ le p \)。在这种情况下,我们得到了一个重要的不等式,并将一些适当的广义最大原理应用于一个合适的Cheng-Yau修饰算子,以获得线性Weingarten子流形的某些特征。

更新日期:2020-10-30
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