Geodesic
On the cut Locus and the Focal Locus of a Submanifold in a Riemannian Manifold II
Publications de l'Institut Mathématique, _N_S_41 (1987) no. 55, p. 119

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Let $M$ be a compact connected Riemannian manifold and let $L$ be a compact connected submanifold of $M$. We show that if a point $x$ is a closest cut point of $L$ which is not a focal point of $L$, then two different minimizing geodesics meet at an angle of $\pi$ at $x$. We also generalize some of the results of [9].
Classification : 53B21 53C40 
@article{PIM_1987_N_S_41_55_a14,
     author = {Hukum Singh},
     title = {On the cut {Locus} and the {Focal} {Locus} of a {Submanifold} in a {Riemannian} {Manifold} {II}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {119 },
     publisher = {mathdoc},
     volume = {_N_S_41},
     number = {55},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1987_N_S_41_55_a14/}
}
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Hukum Singh. On the cut Locus and the Focal Locus of a Submanifold in a Riemannian Manifold II. Publications de l'Institut Mathématique, _N_S_41 (1987) no. 55, p. 119 . http://geodesic.mathdoc.fr/item/PIM_1987_N_S_41_55_a14/