Some remarks on the generalized Myer’s theorems
Keywords:Bakry-Emery Ricci tensor, Index form, Myers-type theorem, Riccati inequality
In this paper, firstly, we prove a generalization of Ambrose (or Myers) theorem for the Bakry-Emery Ricci tensor. Later, we improve previous diameter estimate obtained by Galloway for complete Riemannian manifolds. To obtain these results, we utilize the Riccati inequality and the index form of a minimizing unit speed geodesic segment, respectively.
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