Minimal Lagrangian submanifolds in the complex hyperbolic space
Differential Geometry
2012-12-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0110251,
title = {Minimal Lagrangian submanifolds in the complex hyperbolic space},
author = {I. Castro and C. R. Montealegre and F. Urbano},
journal= {arXiv preprint arXiv:math/0110251},
year = {2012}
}
Comments
28 pages. To appear in Illinois J. Math