# soul (Q4171386)

compact, totally convex, totally geodesic submanifold S of a complete connected Riemannian manifold M such that M is diffeomorphic to the normal bundle of S; it always exists if M has nonnegative sectional curvature (soul theorem)
• soul theorem
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soul
compact, totally convex, totally geodesic submanifold S of a complete connected Riemannian manifold M such that M is diffeomorphic to the normal bundle of S; it always exists if M has nonnegative sectional curvature (soul theorem)
• soul theorem

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