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A Parametrization of Isometric Immersions between Hyperbolic Spaces
Authors:K Abe  H Mori  H Takahashi
Institution:(1) Department of Mathematics, University of Connecticut, U-9, MSB 111, 196, Auditorium Road, Storrs, Connecticut, 06269, U.S.A.;(2) Department of Mathematics, Joetsu University of Education, 943 Joetsu, Niigata Pref., Japan e-mail;(3) Department of Mathematics, Ichinoseki National College of Technology, 021 Ichinoseki, Iwate Pref., Japan
Abstract:We parametrize the space of isometric immersions of the hyperbolic n -space into the hyperbolic ( n +1)-space by a family of properly chosen (at most) countable n -tuples of real-valued functions. This is an answer to the problem posed by Nomizu in 1973. We also construct a one-parameter family of deformable isometric immersions from the quotient spaces of the hyperbolic 2-plane modulo and some totally discontinuous subgroups of isometries.
Keywords:isometric immersion  hyperbolic space form  fundamental theorem for hypersurfaces  linear partial differential equation  Klein group
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