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Isometric immersions from the hyperbolic space  into 
Author(s):
Hu
Ze-Jun;
Zhao
Guo-Song
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2693-2697.
MSC (1991):
Primary 53C42;
Secondary 53C21
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Abstract:
In this paper, we transform the problem of determining isometric immersions from  into  into that of solving a degenerate Monge-Ampère equation on the unit disc. By presenting one family of special solutions to the equation, we obtain a great many noncongruent examples of such isometric immersions with or without umbilic set.
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Additional Information:
Hu
Ze-Jun
Affiliation:
Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, Henan, People's Republic of China
Address at time of publication:
Department of Mathematics, Hangzhou University, Hangzhou, 310028, Zhejiang, People's Republic of China
Zhao
Guo-Song
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People's Republic of China
DOI:
10.1090/S0002-9939-97-03905-1
PII:
S 0002-9939(97)03905-1
Keywords:
Isometric immersion,
hyperbolic space,
Monge-Amp\`ere equation
Received by editor(s):
January 12, 1996
Received by editor(s) in revised form:
April 12, 1996
Additional Notes:
This research was supported by the National Natural Science Foundation of China
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1997,
American Mathematical Society
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