First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow - Azami, Shahroud (Journal of the Indonesian Mathematical Society, 2018)
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 $-Δ_{φ}+cR$ under the Ricci-Bourguignon flow, where $Δ_{φ}$ 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.