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On Singular Distributions With Statistical Structure

Author

Listed:
  • Paul Popescu

    (Department of Applied Mathematics, University of Craiova, Str. Al. Cuza, No, 13, 200585 Craiova, Romania)

  • Vladimir Rovenski

    (Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel)

  • Sergey Stepanov

    (Department of Mathematics, Finance University, 49-55, Leningradsky Prospect, 125468 Moscow, Russia)

Abstract

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.

Suggested Citation

  • Paul Popescu & Vladimir Rovenski & Sergey Stepanov, 2020. "On Singular Distributions With Statistical Structure," Mathematics, MDPI, vol. 8(10), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1825-:d:430593
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    References listed on IDEAS

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    1. Paul Popescu & Vladimir Rovenski & Sergey Stepanov, 2020. "The Weitzenböck Type Curvature Operator for Singular Distributions," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
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