Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$

Ze-Jun Hu

ArticleOriginal scientific text

Title

Isometric immersions of the hyperbolic space $H^{n} (- 1)$ into $H^{n + 1} (- 1)$

Authors ¹

Affiliations

Postdoctoral Station of Mathematics, Hangzhou University, Hangzhou 310028, Zhejiang, People's Republic of China

Abstract

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.

Keywords

ENG

isometric immersion, Monge-Ampère type equation, hyperbolic space

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Title

Isometric immersions of the hyperbolic space Hn(-1) into Hn+1(-1)

Affiliations

Abstract

Keywords

Bibliography

Isometric immersions of the hyperbolic space $H^{n} (- 1)$ into $H^{n + 1} (- 1)$