The Gauss map and second fundamental form of surfaces in a Lie group

DOI10.1007/s10231-015-0540-9zbMath1360.53063arXiv1506.03743OpenAlexW2099011297WikidataQ115385054 ScholiaQ115385054MaRDI QIDQ325957

Abigail Folha, Carlos Peñafiel

Publication date: 11 October 2016

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.03743

zbMATH Keywords

Gauss mapharmonic mapextrinsic curvatureunimodular Lie groups

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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• Weierstrass representation for minimal surfaces in hyperbolic space
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• Kenmotsu type representation formula for surfaces with prescribed mean curvature in the hyperbolic 3-space
• Weierstrass representation for surfaces with prescribed normal Gauss map and Gauss curvature in \(H^3\)
• A Weierstrass type representation for minimal surfaces in Sol
• Constant mean curvature surfaces in metric Lie groups

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