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Isometric immersions from
the hyperbolic space $H^2(-1)$ into $H^3(-1)$


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
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Abstract: In this paper, we transform the problem of determining isometric immersions from $H^2(-1)$ into $H^3(-1)$ 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

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