Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606198 | Differential Geometry and its Applications | 2011 | 9 Pages |
Abstract
Let M be a complete non-compact connected Riemannian n -dimensional manifold. We first prove that, for any fixed point p∈Mp∈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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Kei Kondo, Minoru Tanaka,