The Weitzenböck Type Curvature Operator for Singular Distributions

Paul Popescu, Vladimir Rovenski and Sergey Stepanov
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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, 31905 Haifa, Israel
Sergey Stepanov: Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences, 125190 Moscow, Russia

Mathematics, 2020, vol. 8, issue 3, 1-18

Abstract: 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.

Keywords: Riemannian manifold; singular distribution; Weitzenböck curvature operator; Hodge Laplacian; almost Lie algebroid (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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