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

Abstract

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.

Keywords

• Eigenvalue| Laplace| Ricci-Bourguignon flow| Riemannian manifold| Eigenvector