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Minimal Lagrangian immersions in \(RH^2\times RH^2\). (English) Zbl 1451.53086

Vrancken, L. (ed.), Symposium on the differential geometry of submanifolds, Valenciennes, France, July 3–7, 2007. Valenciennes: Université de Valenciennes; London: Lulu.com. 217-220 (2007).
Summary: A relation, via the Gauss map, between the maximal spacelike surfaces in anti De-Sitter space and minimal Lagrangian immersions in the product of two hyperbolic planes is presented. Using this connection new examples of minimal surfaces invariant under the action of one-parameter groups of isometries are constructed.
For the entire collection see [Zbl 1128.53004].

MSC:

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53D12 Lagrangian submanifolds; Maslov index
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics