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Open AccessArticle

On Singular Distributions With Statistical Structure

by 1, 2,* and 3
1
Department of Applied Mathematics, University of Craiova, Str. Al. Cuza, No, 13, 200585 Craiova, Romania
2
Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel
3
Department of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(10), 1825; https://doi.org/10.3390/math8101825 (registering DOI)
Received: 10 September 2020 / Revised: 3 October 2020 / Accepted: 13 October 2020 / Published: 17 October 2020
(This article belongs to the Special Issue Geometric Methods and their Applications)
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. View Full-Text
Keywords: Riemannian manifold; almost Lie algebroid; singular distribution; statistical structure; Weitzenb枚ck curvature operator; harmonic differential form Riemannian manifold; almost Lie algebroid; singular distribution; statistical structure; Weitzenb枚ck curvature operator; harmonic differential form
MDPI and ACS Style

Popescu, P.; Rovenski, V.; Stepanov, S. On Singular Distributions With Statistical Structure. Mathematics 2020, 8, 1825.

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