First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow - Shahroud Azami (IndoMS, 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.