Qihua Ruan
Abstract
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In this paper, 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.
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In this paper, 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.
Key concepts: Rigidity (electromagnetism), Ricci curvature, Mathematics, Manifold (fluid mechanics), Curvature, Pure mathematics, Curvature of Riemannian manifolds, Ricci-flat manifold