Soul theorem

If (M,g) is a completeComplete space

In mathematical analysis, a metric space M is said to be complete if every Cauchy sequence of points in M has a lim...
 non-compact Riemannian manifoldRiemannian manifold

In Riemannian geometry, a Riemannian manifold is a real differentiable manifold M in which each tangent space is equippe...
 with sectional curvatureSectional curvature

In Riemannian geometry, the sectional curvature is one of the ways to describe the curvature of Riemannian manifolds....
 K ≥ 0, then (M,g) has a compact totally convexGlossary of Riemannian and metric geometry

This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of diffe...
, totally geodesicGlossary of Riemannian and metric geometry Overview

This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of diffe...
 submanifoldGlossary of differential geometry and topology

This is a glossary of terms specific to differential geometry and differential topology....
 S such that M is diffeomorphic to the normal bundleGlossary of Riemannian and metric geometry

This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of diffe...
 of S.

Soul conjecture

Suppose M is complete and noncompact with sectional curvature K ≥ 0, with holding at some point. Then the soul of M has to be a point; equivalently M is diffeomorphic to .