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

Ze-Jun Hu (1999)

Colloquium Mathematicae

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.

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