(1) Instituto de Matemática, Universidade Federal Fluminense (UFF), Rua Mário Santos Braga S/N. Valonguinho, 24.020-140 Niterói, RJ, Brazil
Abstract:
We prove new ergodic theorems in the context of infinite ergodic theory, and give some applications to Riemannian and Kähler manifolds without conjugate points. One of the consequences of these ideas is that a complete manifold without conjugate points has nonpositive integral of the infimum of Ricci curvatures, whenever this integral makes sense. We also show that a complete Kähler manifold with nonnegative holomorphic curvature is flat if it has no conjugate points.