Monotonicity of eigenvalues of Witten-Laplace operator along the Ricci-Bourguignon flow

AIMS Mathematics

Shahroud Azami¹ 

关键词: : ;    Eigenvalue;    Laplace;    Ricci-Bourguignon flow;    Riemannian manifold;    Eigenvector;   

DOI  :  10.3934/Math.2017.2.230

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

In this article we will investigate monotonicity for the first eigenvalue problem of the Witten-Laplace operator acting on the space of functions along the Ricci-Bourguignon flow on closed manifolds. We find the first variation formula for the eigenvalues of Witten-Laplacian on a closed manifold evolving by the Ricci-Bourguignoni flow and construct various monotonic quantities. At the end we find some applications in 2-dimensional and 3-dimensional manifolds and give an example.

【 授权许可】

CC BY