Bilaplacian on a Riemannian manifold and Levi-Civita connection

Relationship between stochastic flows and connection forms

In this article I will prove new representation for the Levi-Civita connection in terms of the stochastic flow corresponding to Brownian motion on manifold.

从主方程中的互易关系出发的概率流形几何计算

Geometric calculations on probability manifolds from reciprocal relations in Master equations

本文从主方程互易关系出发，研究概率流形的几何计算，推导了Levi-Civita连接、梯度等算子，并给出了两个具体例子。