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arXiv · 2008.12868

On the Bochner technique for singular distributions

Paul Popescu·Vladimir Rovenski·Sergey Stepanov
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Abstract

In this paper we continue our recent study of a manifold endowed with a singular or regular distribution, determined as the image of the tangent bundle under a smooth endomorphism, and generalize Bochner's technique to the case of a distribution with a statistical type structure. Following the theory of statistical structures on Riemannian manifolds and construction of an almost Lie algebroid on a vector bundle, we define the modified statistical connection and exterior derivative on tensors. Then we introduce the Weitzenbock type curvature operator on tensors and derive the Bochner-Weitzenbock type formula. These allow us to obtain vanishing theorems about the null space of the Hodge type Laplacian on a distribution.

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Paul Popescu, Vladimir Rovenski, Sergey Stepanov. 2020-08-28. On the Bochner technique for singular distributions. https://arxiv.org/abs/2008.12868

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