Geodesic
Intersections of Quadrics, Moment-Angle Manifolds, and Hamiltonian-Minimal Lagrangian Embeddings
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 1, pp. 47-61

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We study the topology of Hamiltonian-minimal Lagrangian submanifolds $N$ in $\mathbb{C}^m$ constructed from intersections of real quadrics in a work of the first author. This construction is linked via an embedding criterion to the well-known Delzant construction of Hamiltonian toric manifolds. We establish the following topological properties of $N$: every $N$ embeds as a submanifold in the corresponding moment-angle manifold $\mathcal Z$, and every $N$ is the total space of two different fibrations, one over the torus $T^{m-n}$ with fiber a real moment-angle manifold $\mathcal{R}$ and the other over a quotient of $\mathcal{R}$ by a finite group with fiber a torus. These properties are used to produce new examples of Hamiltonian-minimal Lagrangian submanifolds with quite complicated topology.
Keywords: moment-angle manifold, simplicial fan, simple polytope. 
@article{FAA_2013_47_1_a4,
     author = {A. E. Mironov and T. E. Panov},
     title = {Intersections of {Quadrics,} {Moment-Angle} {Manifolds,} and {Hamiltonian-Minimal} {Lagrangian} {Embeddings}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {47--61},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_1_a4/}
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A. E. Mironov; T. E. Panov. Intersections of Quadrics, Moment-Angle Manifolds, and Hamiltonian-Minimal Lagrangian Embeddings. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 1, pp. 47-61. http://geodesic.mathdoc.fr/item/FAA_2013_47_1_a4/