The structure of manifolds of nonnegative sectional curvature
Understanding the structure of a Riemannian Manifold based on information about its sectional curvature is a challenging problem which has received much attention. According to the Soul Theorem any complete noncompact Riemannian manifold M of nonnegative sectional curvature contains a compact totall...
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| Language: | English |
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University of British Columbia
2011
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| Online Access: | http://hdl.handle.net/2429/31554 |
| Summary: | Understanding the structure of a Riemannian Manifold based on information about its sectional curvature is a challenging problem which has received much attention. According to the Soul Theorem any complete noncompact Riemannian manifold M of nonnegative sectional curvature contains a compact totally geodesic submanifold called the soul of M. Furthermore, the manifold is diffeomorphic to the normal bundle of the soul. This is a beautiful structural result which provides a significant contribution to the classification of Riemannian manifolds. In this paper we present a complete proof of the Soul Theorem which draws upon the theory and techniques developed over the years since its original proof in 1972. The proof relies heavily upon results from Comparison Geometry and the theory of convex sets. === Science, Faculty of === Mathematics, Department of === Graduate |
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