AIMS Mathematics, 2017, 2(2): 230-243. doi: 10.3934/Math.2017.2.230

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

Department of Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran.

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.
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