Isometric immersions from the hyperbolic space $H^2(-1)$ into $H^3(-1)$
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- by Hu Ze-Jun and Zhao Guo-Song PDF
- Proc. Amer. Math. Soc. 125 (1997), 2693-2697 Request permission
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.References
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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
- MR Author ID: 346519
- ORCID: 0000-0003-2744-5803
- Zhao Guo-Song
- Affiliation: Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China
- 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 1997 American Mathematical Society
- 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