Eigenvalues of the Dirac operator on compact spin manifolds under Ricci flow

Abstract

In this paper, we first derive the evolution formula for the square of the first eigenvalue λ2 of the Dirac operator under the metric flow ∂∂tg=h on compact spin manifolds. We then prove that λ2 is nondecreasing under the Ricci flow on compact spin surfaces with non-negative Gauss curvature.