First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow

Shahroud Azami (1)
(1) , Iran, Islamic Republic of

Abstract

Let $(M,g(t))$ be a compact Riemannian manifold  and  the metric $g(t)$ evolve by the Ricci-Bourguignon flow. We find the formula variation of the eigenvalues of  geometric operator $-\Delta_{\phi}+cR$ under  the Ricci-Bourguignon flow, where  $\Delta_{\phi}$  is the Witten-Laplacian operator and $R$ is the scalar curvature. In the final  we show that some quantities dependent to the eigenvalues of  the geometric operator are  nondecreasing along the Ricci-Bourguignon flow on  closed manifolds  with nonnegative curvature.

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Authors

Shahroud Azami
azami@sci.ikiu.ac.ir (Primary Contact)
Azami, S. (2017). First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow. Journal of the Indonesian Mathematical Society, 24(1), 51–60. https://doi.org/10.22342/jims.24.1.434.51-60
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