Minimal Lagrangian submanifolds in the complex hyperbolic space

Details Minimal Lagrangian submanifolds in the complex hyperbolic space Minimal Lagrangian submanifolds in the complex hyperbolic space

2001-10-23

arxiv.org/abs/math/0110251v1

Mathematics

Differential Geometry

28 pages. To appear in Illinois J. Math

Scientific paper

In this paper we construct new examples of minimal Lagrangian submanifolds in the complex hyperbolic space with large symmetry groups, obtaining three 1-parameter families with cohomegeneity one. We characterize them as the only minimal Lagrangian submanifolds in CH^n foliated by umbilical hypersurfaces of Lagrangian subspaces RH^n of CH^n. Several suitable generalizations of the above construction allow us to get new families of minimal Lagrangian submanifolds in CH^n from curves in CH^1 and (n-1)-dimensional minimal Lagrangian submanifolds of the complex space forms CP^n-1, CH^n-1 and C^n-1. Similar constructions are made in the complex projective space.

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