Ricci curvature,radial curvature and large volume growth |
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Authors: | Guanghan Li Yi Shi Chuanxi Wu |
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Institution: | 1.School of Mathematics and Computer Science, and Key Laboratory of Applied Mathematics of Hubei Province,Hubei University,Wuhan,China;2.Department of Mathematics,Hubei University,Wuhan,China;3.Institute of Mathematics,Hubei University,Wuhan,China |
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Abstract: | In this paper, we study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. When the Ricci curvature
is nonnegative, we show that this kind of manifolds are diffeomorphic to a Euclidean space, by assuming an upper bound on
the radial curvature and a volume growth condition of their geodesic balls. When the Ricci curvature only has a lower bound,
we also prove that such a manifold is diffeomorphic to a Euclidean space if the radial curvature is bounded from below. Moreover,
by assuming different conditions and applying different methods, we shall prove more results on Riemannian manifolds with
large volume growth. |
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Keywords: | |
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