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On Row Sequences of Hermite–Padé Approximation and Its Generalizations
Open AccessArticle

The Weitzenböck Type Curvature Operator for Singular Distributions

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, 31905 Haifa, Israel
3
Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences, 125190 Moscow, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 365; https://doi.org/10.3390/math8030365
Received: 16 February 2020 / Revised: 1 March 2020 / Accepted: 3 March 2020 / Published: 6 March 2020
(This article belongs to the Special Issue Geometric Structures and Interdisciplinary Applications)
We study geometry of a Riemannian manifold endowed with a singular (or regular) distribution, determined as an image of the tangent bundle under smooth endomorphisms. Following construction of an almost Lie algebroid on a vector bundle, we define the modified covariant and exterior derivatives and their L 2 adjoint operators on tensors. Then, we introduce the Weitzenböck type curvature operator on tensors, prove the Weitzenböck type decomposition formula, and derive the Bochner–Weitzenböck type formula. These allow us to obtain vanishing theorems about the null space of the Hodge type Laplacian. The assumptions used in the results are reasonable, as illustrated by examples with f-manifolds, including almost Hermitian and almost contact ones. View Full-Text
Keywords: Riemannian manifold; singular distribution; Weitzenböck curvature operator; Hodge Laplacian; almost Lie algebroid Riemannian manifold; singular distribution; Weitzenböck curvature operator; Hodge Laplacian; almost Lie algebroid
MDPI and ACS Style

Popescu, P.; Rovenski, V.; Stepanov, S. The Weitzenböck Type Curvature Operator for Singular Distributions. Mathematics 2020, 8, 365.

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