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A Parametrization of Isometric Immersions between Hyperbolic Spaces (1997)

Abe, K. ; Mori, H. ; Takahashi, H.

Springer

Geometriae dedicata 65 (1997), S. 31-46

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ISSN: 1572-9168

Keywords: isometric immersion ; hyperbolic space form ; fundamental theorem for hypersurfaces ; linear partial differential equation ; Klein group

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1004960317128

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