论文标题
在Bochner的奇异分布技术上
On the Bochner technique for singular distributions
论文作者
论文摘要
在本文中，我们继续对具有奇异或规则分布的歧管进行研究，这是在光滑的内态下的切线束的图像，并将Bochner的技术推广到具有统计类型结构的分布的情况下。遵循有关riemannian流形的统计结构理论，并在矢量束上几乎躺着代数的构造，我们定义了张量的修改后的统计连接和外部导数。然后，我们在张量上介绍Weitzenbock类型曲率算子，并推导Bochner-Weitzenbock型公式。这些使我们能够在分布中获得有关霍奇型laplacian的空空间的消失定理。
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.
