Isometric immersions of the hyperbolic space $H^n(-1)$ into $H^{n+1}(-1)$
Volume 79 / 1999
Colloquium Mathematicum 79 (1999), 17-23
DOI: 10.4064/cm-79-1-17-23
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.
