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Two rigidity theorems on manifolds with Bakry-Emery Ricci curvature. (English) Zbl 1170.53024

Summary: We generalize the Cheng’s maximal diameter theorem and Bishop volume comparison theorem to the manifold with the Bakry-Emery Ricci curvature. As their applications, we obtain some rigidity theorems on the warped product.

MSC:

53C24 Rigidity results
53C20 Global Riemannian geometry, including pinching
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