Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary

Abstract

Let $M$ be a connected, complete Riemannian manifold with (possibly empty) boundary $\partial M$ . Cheeger and Gromoll proved in From this result, they showed that $M$ as above is the isometric product $N\cross R^{k}(k\geqq 0)$ , where $N$ contains no lines and $R^{k}$ has its standard flat metric. They also proved in Later, making use of this result, Burago and Zalgaller obtained in