• Corpus ID: 119323395

# Minimal and Hamiltonian-minimal submanifolds in toric geometry

@article{Kotelskiy2013MinimalAH,
title={Minimal and Hamiltonian-minimal submanifolds in toric geometry},
author={Artem Kotelskiy},
journal={arXiv: Symplectic Geometry},
year={2013}
}
In this paper we investigate a family of Hamiltonian-minimal Lagrangian submanifolds in ${\mathbb C}^m$, ${\mathbb C}P^m$ and other symplectic toric manifolds constructed from intersections of real quadrics. In particular, we explain the nature of this phenomenon by proving H-minimality in a more conceptual way, and prove minimality of the same submanifolds in the corresponding moment-angle manifolds.
4 Citations
Zoo of monotone Lagrangians in $\mathbb{C}P^n$
Let P ⊂ Rm be a polytope of dimension m with n facets and a1, . . . , an be the normal vectors to the facets of P . Assume that P is Delzant, Fano, and a1 + . . . + an = 0. We associate a monotone
Zoo of monotone Lagrangians in C
Let P ⊂ Rm be a polytope of dimension m with n facets and a1, . . . , an be the normal vectors to the facets of P . Assume that P is Delzant, Fano, and a1 + . . . + an = 0. We associate a monotone
Monotone Lagrangian submanifolds of $\mathbb{C}^n$ and toric topology
Let $\mathcal{N}$ be the total space of a bundle over some $k$-dimensional torus with fibre $\mathcal{R}$, where $\mathcal{R}$ is diffeomorphic to $S^k \times S^l$, or $S^k \times S^l \times S^m$, or
Non-isotopic monotone Lagrangian submanifolds of $\mathbb{C}^n$
Let $P$ be a Delzant polytope in $\mathbb{R}^k$ with $n+k$ facets. We associate a closed Lagrangian submanifold $L$ of $\mathbb{C}^n$ to each Delzant polytope. We prove that $L$ is monotone if and

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