Constant mean curvature surfaces in hyperbolic 3-space via loop groups
-
Josef F. Dorfmeister
,
Jun-ichi Inoguchi
Abstract.
In hyperbolic 3-space 
surfaces of constant
mean curvature H come in three types, corresponding to the cases
, 
, 
.
Via the Lawson correspondence the latter two cases
correspond to constant mean curvature surfaces in Euclidean
3-space 
with 
and 
, respectively.
These surface classes have been investigated intensively
in the literature. For the case there is
no Lawson correspondence in Euclidean space and there
are relatively few publications. Examples have been difficult
to construct. In this paper we present a generalized Weierstrass type
representation for surfaces of constant mean curvature in
with particular emphasis on
the case of mean curvature .
In particular, the generalized Weierstrass type
representation presented in this paper enables us to
construct simultaneously minimal surfaces
() and non-minimal constant mean curvature surfaces (
).
© 2014 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Constant mean curvature surfaces in hyperbolic 3-space via loop groups
- La formule des traces pour les revêtements de groupes réductifs connexes. I. Le développement géométrique fin
- Heegner cycles and derivatives of p-adic L-functions
- On Chow motives of surfaces
- The locus of real multiplication and the Schottky locus
- Stability of the positive mass theorem for rotationally symmetric Riemannian manifolds
- Real trigonal curves and real elliptic surfaces of type I
