Isometric immersions from

the hyperbolic space into

Authors:
Hu Ze-Jun and Zhao Guo-Song

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2693-2697

MSC (1991):
Primary 53C42; Secondary 53C21

DOI:
https://doi.org/10.1090/S0002-9939-97-03905-1

MathSciNet review:
1397002

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-97-03905-1

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

Article copyright:
© Copyright 1997
American Mathematical Society