Geodesic
Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$
Colloquium Mathematicum, Tome 79 (1999) no. 1, pp. 17-23

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We transform the problem of determining isometric immersions from $H^n(-1)$ into $H^{n+1}(-1)$ into that of solving equations of degenerate Monge-Ampère type on the unit ball $B^n(1)$. By presenting one family of special solutions to the equations, we obtain a great many noncongruent examples of such isometric immersions with or without umbilic set.
DOI : 10.4064/cm-79-1-17-23
Keywords: isometric immersion, Monge-Ampère type equation, hyperbolic space

Ze-Jun Hu 1

1 
@article{10_4064_cm_79_1_17_23,
     author = {Ze-Jun Hu},
     title = {Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$},
     journal = {Colloquium Mathematicum},
     pages = {17--23},
     publisher = {mathdoc},
     volume = {79},
     number = {1},
     year = {1999},
     doi = {10.4064/cm-79-1-17-23},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-79-1-17-23/}
}
TY  - JOUR
AU  - Ze-Jun Hu
TI  - Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$
JO  - Colloquium Mathematicum
PY  - 1999
SP  - 17
EP  - 23
VL  - 79
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm-79-1-17-23/
DO  - 10.4064/cm-79-1-17-23
LA  - en
ID  - 10_4064_cm_79_1_17_23
ER  - 
%0 Journal Article
%A Ze-Jun Hu
%T Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$
%J Colloquium Mathematicum
%D 1999
%P 17-23
%V 79
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm-79-1-17-23/
%R 10.4064/cm-79-1-17-23
%G en
%F 10_4064_cm_79_1_17_23
Ze-Jun Hu. Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$. Colloquium Mathematicum, Tome 79 (1999) no. 1, pp. 17-23. doi: 10.4064/cm-79-1-17-23

Cité par Sources :