Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces |
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Authors: | Kei Kondo Minoru Tanaka |
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Institution: | Department of Mathematics, Tokai University, Hiratsuka City, Kanagawa Pref. 259-1292, Japan |
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Abstract: | Let M be a complete non-compact connected Riemannian n-dimensional manifold. We first prove that, for any fixed point p∈M, the radial Ricci curvature of M at p is bounded from below by the radial curvature function of some non-compact n-dimensional model. Moreover, we then prove, without the pointed Gromov-Hausdorff convergence theory, that, if model volume growth is sufficiently close to 1, then M is diffeomorphic to Euclidean n-dimensional space. Hence, our main theorem has various advantages of the Cheeger-Colding diffeomorphism theorem via the Euclidean volume growth. Our main theorem also contains a result of do Carmo and Changyu as a special case. |
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Keywords: | primary 53C21 secondary 53C22 |
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