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On Singular Distributions With Statistical Structure
Mathematics ( IF 2.4 ) Pub Date : 2020-10-17 , DOI: 10.3390/math8101825
Paul Popescu , Vladimir Rovenski , Sergey Stepanov

In this paper, we extend our previous study regarding a Riemannian manifold endowed with a singular (or regular) distribution, generalizing Bochner’s technique and a statistical structure. Following the construction of an almost Lie algebroid, we define the central concept of the paper: The Weitzenböck type curvature operator on tensors, prove the Bochner–Weitzenböck type formula and obtain some vanishing results about the null space of the Hodge type Laplacian on a distribution.

中文翻译:

具有统计结构的奇异分布

在本文中,我们扩展了关于具有奇异(或正则)分布的黎曼流形的先前研究,并推广了Bochner的技术和统计结构。在构造了一个几乎为李的代数之后,我们定义了本文的中心概念:张量上的Weitzenböck型曲率算子,证明Bochner–Weitzenböck型公式并获得关于分布上Hodge型Laplacian的零空间的一些消失的结果。
更新日期:2020-10-17
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