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The Bakry-Emery Ricci tensor and its applications to some compactness theorems
(Springer, 2012)Let (M, g) be a complete and connected Riemannian manifold of dimension n. By using the Bakry-Emery Ricci curvature tensor on M, we prove two theorems which correspond to the Myers compactness theorem. -
Modifications of the Ricci tensor and applications
(Birkhauser Verlag Ag, 2010)By using two modified Ricci tensors, we prove some theorems which correspond to Myers's diameter estimate theorem and Bochner's vanishing theorem.