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Pseudotoric structures and Lagrangian spheres in the flag variety \(F^3\). (English. Russian original) Zbl 1316.53086

Math. Notes 96, No. 3, 458-461 (2014); translation from Mat. Zametki 96, No. 3, 476-479 (2014).
The author proves the following result: Any smooth path on the projective line \(L\) which has endpoints \(p_i\) and \(p_j\) and does not pass through \(p_k\) determines a Lagrangian embedding of \(S^3\) in \(F^3\).

MSC:

53D12 Lagrangian submanifolds; Maslov index
14M15 Grassmannians, Schubert varieties, flag manifolds
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References:

[1] Tyurin, N. A., No article title, Teor. Mat. Fiz., 167, 193 (2011) · doi:10.4213/tmf6633
[2] Tyurin, N. A., No article title, Teor. Mat. Fiz., 162, 307 (2010) · doi:10.4213/tmf6473
[3] S. K. Donaldson, in Mathematics: Frontiers and Perspectives (Amer. Math. Soc., Providence, RI, 2000), pp. 55-64. · Zbl 0958.57027
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