2020/08/28 by Paul Popescu, Popescu, Paul, Vladimir Rovenski +4
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Lipid metabolism and disorders #math.DG
paper · pdf · doi:10.48550/arxiv.2008.12868
19 pages
arxiv created 2020/08/28 · openalex publication_date 2020/08/28 · arxiv updated 2020/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.