On quadratic differentials and twisted normal maps of surfaces in \(\mathbb S^2 \times\mathbb R\) and \(\mathbb H^2\times\mathbb R\)

DOI10.1007/s00025-011-0151-8zbMath1341.53092OpenAlexW2090491788MaRDI QIDQ1758363

Maria Luiza Leite, Jaime Bruck Ripoll

Publication date: 9 November 2012

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-011-0151-8

zbMATH Keywords

harmonic mapholomorphic differentialtwisted normal

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Differential geometric aspects of harmonic maps (53C43) Non-Euclidean differential geometry (53A35) Geometric function theory (30C99)

Related Items (4)

The Gauss map of minimal surfaces in \({\mathbb{S}}^2 \times{\mathbb{R}} \) ⋮ Harmonic Gauss maps of submanifolds of arbitrary codimension of the Euclidean space and sphere and some applications ⋮ An extension of Ruh-Vilms’ theorem to hypersurfaces in symmetric spaces and some applications ⋮ Generalized Weierstrass representation for surfaces in Heisenberg spaces

Cites Work

• Surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times \mathbb R\) with holomorphic Abresch-Rosenberg differential
• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Differential geometry in the large. Seminar lectures New York University 1946 and Stanford University 1956. With a preface by S. S. Chern
• Gauss map harmonicity and mean curvature of a hypersurface in a homogeneous manifold
• A characterization of constant mean curvature surfaces in homogeneous 3-manifolds
• A Report on Harmonic Maps
• The Tension Field of the Gauss Map
• Harmonic maps and constant mean curvature surfaces in H 2 x R

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