An analogue of minimal surface theory in 𝑆𝐿(𝑛,𝐂)/𝐒𝐔(𝐧)

DOI10.1090/S0002-9947-01-02935-XzbMath1005.53053arXivmath/0008016OpenAlexW1678701330MaRDI QIDQ2781362

Masaro Takahashi, Masatoshi Kokubu, Masaaki Umehara, Kotaro Yamada

Publication date: 19 March 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0008016

zbMATH Keywords

submanifoldssymmetric spaceRiemann surfacerepresentation formulacomplex semisimple Lie groupconformal immersionChern-Ossermann type inequalityholomorphic right Gauss map

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Non-Euclidean differential geometry (53A35)

Related Items (3)

Integrable deformation of critical surfaces in spaceforms ⋮ Spinorial representation of submanifolds in \(\mathrm{SL}_n(\mathbb{C})/\mathrm{SU}(n)\) ⋮ Marginally trapped surfaces in \(\mathbb L^4\) and an extended Weierstrass-Bryant representation

Cites Work

• The inverse surface and the Osserman inequality
• A duality on CMC-1 surfaces in hyperbolic space, and a hyperbolic analogue of the Osserman inequality
• Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus
• Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space
• Surfaces of constant mean curvature \(c\) in \(H^ 3(-c^ 2)\) with prescribed hyperbolic Gauss map
• Complete minimal surfaces in Euclidean \(n\)-spaces
• On a class of conformal metrics, with application to differential geometry in the large
• A parametrization of the Weierstrass formulae and perturbation of complete minimal surfaces in R3 into the hyperbolic 3-space.
• The value distribution of the hyperbolic Gauss map
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