# Manifold contains a totally geodesic closed hypersurface

Let $(M^n,g)$ be a closed simply-connected positively curved manifold. Show that if $M$ contains a totally geodesic closed hypersurface (i.e., the second fndamental form or shape operator is zero), then $M$ is homeomorpic to a sphere.

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What have you tried? –  Jason DeVito Jul 5 '12 at 2:49