Artículo
The Gauss map of surfaces in PSL˜2(R)
Autor/es | Daniel, Benoit
Fernández Delgado, Isabel Mira, Pablo |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2015 |
Fecha de depósito | 2020-02-20 |
Publicado en |
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Resumen | We define a Gauss map for surfaces in the universal cover of the
Lie group PSL2(R) endowed with a left-invariant Riemannian metric having
a 4-dimensional isometry group. This Gauss map is not related to the Lie
group ... We define a Gauss map for surfaces in the universal cover of the Lie group PSL2(R) endowed with a left-invariant Riemannian metric having a 4-dimensional isometry group. This Gauss map is not related to the Lie group structure. We prove that the Gauss map of a nowhere vertical surface of critical constant mean curvature is harmonic into the hyperbolic plane H2 and we obtain a Weierstrass-type representation formula. This extends results in H2 ×R and the Heisenberg group Nil3, and completes the proof of existence of harmonic Gauss maps for surfaces of critical constant mean curvature in any homogeneous manifold diffeomorphic to R3 with isometry group of dimension at least 4. |
Identificador del proyecto | MTM2010-19821
P09-FQM-5088 |
Cita | Daniel, B., Fernández Delgado, I. y Mira, P. (2015). The Gauss map of surfaces in PSL˜2(R). Calculus of Variations and Partial Differential Equations, 52 (3-4), 507-528. |
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