Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Abstract:
The soul theorem states that any open Riemannian manifold with nonnegative sectional curvature contains a totally geodesic compact submanifold such that is diffeomorphic to the normal bundle of . In this paper we show how to modify into a new metric so that:
has nonnegative sectional curvature and soul .
The normal exponential map of is a diffeomorphism.
splits as a product outside of a compact set.
As a corollary we obtain that any such is diffeomorphic to the interior of a convex set in a compact manifold with nonnegative sectional curvature.