The Bonnet problem for surfaces in homogeneous 3-manifolds

DOI10.4310/CAG.2008.V16.N5.A1zbMath1170.53034arXivmath/0612766OpenAlexW1964313070MaRDI QIDQ1011991

J. Martínez

Publication date: 14 April 2009

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612766

zbMATH Keywords

minimal surfaceprincipal curvaturehelicoidal surfacesBonnet problem4-dimensional isometric groupFirst fundamental formRiemannian homogeneous 3-manifold

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Global submanifolds (53C40)

Related Items (11)

HELICOIDAL MINIMAL SURFACES IN ℍ²×ℝ ⋮ Bonnet and isotropically isothermic surfaces in 4-dimensional space forms ⋮ Willmore surfaces and Hopf tori in homogeneous 3-manifolds ⋮ On the moduli space of isometric surfaces with the same mean curvature in 4-dimensional space forms ⋮ Conjugate plateau constructions in product spaces ⋮ Infinitesimally Bonnet bendable hypersurfaces ⋮ Rigidity of convex surfaces in the homogeneous spaces ⋮ The Gauss map of surfaces in \(\widetilde{\mathrm {PSL}}_2(\mathbb R)\) ⋮ Lagrangian Bonnet Problems in complex space forms ⋮ The Bonnet problem for harmonic maps to the three-sphere ⋮ Isoparametric surfaces in $E(\kappa,\tau)$-spaces

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