In mathematics, the soul theorem is the following theorem of Riemannian geometry: If (M,g) is a complete non-compact Riemannian manifold with sectional curvature K ≥ 0, then (M,g) has a compact totally convex, totally geodesic submanifold S such that M is diffeomorphic to the normal bundle of S. The submanifold S is called a soul of (M, g). The soul is not uniquely determined, but any two souls are isometric.
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- In mathematics, the soul theorem is the following theorem of Riemannian geometry: If (M,g) is a complete non-compact Riemannian manifold with sectional curvature K ≥ 0, then (M,g) has a compact totally convex, totally geodesic submanifold S such that M is diffeomorphic to the normal bundle of S. The submanifold S is called a soul of (M, g). The soul is not uniquely determined, but any two souls are isometric. Cheeger and Gromoll (1972) proved the theorem by generalizing a result of Gromoll and Meyer (1969).
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- In mathematics, the soul theorem is the following theorem of Riemannian geometry: If (M,g) is a complete non-compact Riemannian manifold with sectional curvature K ≥ 0, then (M,g) has a compact totally convex, totally geodesic submanifold S such that M is diffeomorphic to the normal bundle of S. The submanifold S is called a soul of (M, g). The soul is not uniquely determined, but any two souls are isometric.
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![[RDF Data]](/statics/sw-cube.png)
