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Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings. (English. Russian original) Zbl 1282.53066
Funct. Anal. Appl. 47, No. 1, 38-49 (2013); translation from Funkts. Anal. Prilozh. 47, No. 1, 47-61 (2013).
In [A. E. Mironov, Sb. Math. 195, No. 1, 85–96 (2004); translation from Mat. Sb. 195, No. 1, 89–102 (2004; Zbl 1078.53079)] a method for constructing H-minimal Lagrangian immersions \(N\rightarrow \mathbb C^n\) from intersections of real quadrics was given. In the paper under review criteria for the map \(N\rightarrow \mathbb C^n\) to be an embedding are given. \(N\rightarrow \mathbb C^n\) is an embedding if and only if the polytope corresponding to the intersection of real quadrics from which \(N\) is constructed is Delzant. Moreover, it is shown that \(N\) is the total space of two fiber bundles, one over a torus and one over a small cover. The above construction is used to construct examples of H-minimal Lagrangian submanifolds of \(\mathbb C^n\) with complicated topology.

MSC:
53D12 Lagrangian submanifolds; Maslov index
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References:
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