On extensions of Myers' theorem


Let M be a compact Riemannian manifold and h a smooth function on M. Let h (x) = inf jvj=1 (Ric x (v; v) ? 2Hess(h) x (v; v)). Here Ric x denotes the Ricci curvature at x and Hess(h) is the Hessian of h. Then M has nite fundamental group if h ? h < 0. Here h =: + 2L rh is the Bismut-Witten Laplacian. This leads to a quick proof of recent results on… (More)