Eigenvalues of the Laplace operator with potential under the backward Ricci flow on locally homogeneous 3-manifolds

Songbo Hou, Shusen Yang

Let $\lambda (t)$ be the first eigenvalue of $-\Delta +aR(a>0)$ under the backward Ricci flow on locally homogeneous 3-manifolds, where $R$ is the scalar curvature. In the Bianchi case, we g…