Geodesic
On the Differentiability of a Distance Function
Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 65 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $M$ be a simply connected complete Kähler manifold and $N$ a closed complete totally geodesic complex submanifold of $M$ such that every minimal geodesic in $N$ is minimal in $M$. Let $U_\nu$ be the unit normal bundle of $N$ in $M$. We prove that if a distance function $\rho$ is differentiable at $v\in U_\nu$, then $\rho$ is also differentiable at $-v$.
DOI : 10.2298/PIM0897065P
Classification : 53C22, 53C55
Keywords: distance function, differentiability, minimal geodesic 
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     title = {On the {Differentiability} of a {Distance} {Function}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {65 },
     publisher = {mathdoc},
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     year = {2008},
     doi = {10.2298/PIM0897065P},
     zbl = {1199.53097},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0897065P/}
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Kwang-Soon Park. On the Differentiability of a Distance Function. Publications de l'Institut Mathématique, _N_S_83 (2008) no. 97, p. 65 . doi : 10.2298/PIM0897065P. http://geodesic.mathdoc.fr/articles/10.2298/PIM0897065P/

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