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 
@article{10_2298_PIM0897065P,
     author = {Kwang-Soon Park},
     title = {On the {Differentiability} of a {Distance} {Function}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {65 },
     publisher = {mathdoc},
     volume = {_N_S_83},
     number = {97},
     year = {2008},
     doi = {10.2298/PIM0897065P},
     zbl = {1199.53097},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0897065P/}
}
TY  - JOUR
AU  - Kwang-Soon Park
TI  - On the Differentiability of a Distance Function
JO  - Publications de l'Institut Mathématique
PY  - 2008
SP  - 65 
VL  - _N_S_83
IS  - 97
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM0897065P/
DO  - 10.2298/PIM0897065P
LA  - en
ID  - 10_2298_PIM0897065P
ER  - 
%0 Journal Article
%A Kwang-Soon Park
%T On the Differentiability of a Distance Function
%J Publications de l'Institut Mathématique
%D 2008
%P 65 
%V _N_S_83
%N 97
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM0897065P/
%R 10.2298/PIM0897065P
%G en
%F 10_2298_PIM0897065P
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

Cité par Sources :