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Fall 2002 Minimal Lagrangian submanifolds in the complex hyperbolic space
Ildefonso Castro, Cristina R. Montealegre, Francisco Urbano
Illinois J. Math. 46(3): 695-721 (Fall 2002). DOI: 10.1215/ijm/1258130980

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 cohomogeneity one. We characterize these submanifolds as the only minimal Lagrangian submanifolds in $\mathbb{C}\mathbb{H}^n$ that are foliated by umbilical hypersurfaces of Lagrangian subspaces $\mathbb{R}\mathbb{H}^n$ of $\mathbb{C}\mathbb{H}^n$. By suitably generalizing this construction, we obtain new families of minimal Lagrangian submanifolds in $\mathbb{C}\mathbb{H}^n$ from curves in $\mathbb{C}\mathbb{H}^1$ and $(n-1)$-dimensional minimal Lagrangian submanifolds of the complex space forms $\mathbb{C}\mathbb{P}^{n-1}$, $\mathbb{C}\mathbb{H}^{n-1}$ and $\mathbb{C}^{n-1}$. We give similar constructions in the complex projective space $\mathbb{C}\mathbb{P}^n$.

Citation

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Ildefonso Castro. Cristina R. Montealegre. Francisco Urbano. "Minimal Lagrangian submanifolds in the complex hyperbolic space." Illinois J. Math. 46 (3) 695 - 721, Fall 2002. https://doi.org/10.1215/ijm/1258130980

Information

Published: Fall 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1032.53052
MathSciNet: MR1951236
Digital Object Identifier: 10.1215/ijm/1258130980

Subjects:
Primary: 53C42
Secondary: 53D12

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 3 • Fall 2002
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