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Helicoidal minimal surfaces in hyperbolic space

Published online by Cambridge University Press:  22 January 2016

Jaime B. Ripoll
Jaime B. Ripoll*
Affiliation:
Universidade Federal do Rio Grande do Sul, Instituto de Matemática, Av. Bento Gonçalves, 9500, 91. 500-Porto Alegre-RS, Brazil
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Denote by H3 the 3-dimensional hyperbolic space with sectional curvatures equal to – 1, and let g be a geodesic in H3 Let {ψt} be the translation along g (see § 2) and let {φt} be the one-parameter subgroup of isometries of H3 whose orbits are circles centered on g. Given any α ∊ R, one can show that λ = {λt} = ψt ∘ φαt} is a one-parameter subgroup of isometries of H3 (see § 2) which is called a helicoidal group of isometries with angular pitch α. Any surface in H3 which is λ-invariant is called a helicoidal surface.

In this work we prove some results concerning minimal helicoidal surfaces in H3. The first one reads:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 114 , June 1989 , pp. 65 - 75
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

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