Special Lagrangian linear subspaces in product symplectic space

Małgorzata Mikosz

Banach Center Publications, Tome 65 (2004), p. 151-156 / Harvested from The Polish Digital Mathematics Library

Résumé

The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism $f : (ℝ^{2 n}, σ = \sum_{i = 1}^{n} d x_{i} \land d y_{i}) \to (ℝ^{2 n}, σ)$ to be a special Lagrangian linear subspace in $(ℝ^{2 n} \times ℝ^{2 n}, ω = π * ₂ σ - π * ₁ σ)$ . This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian $S Λ_{2 n} ≃ S U (2 n) / S O (2 n)$ is defined.

Publié le : 2004-01-01

Zbl 1056.53049

EUDML-ID : urn:eudml:doc:281629

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     title = {Special Lagrangian linear subspaces in product symplectic space},
     journal = {Banach Center Publications},
     volume = {65},
     year = {2004},
     pages = {151-156},
     zbl = {1056.53049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-11}
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Małgorzata Mikosz. Special Lagrangian linear subspaces in product symplectic space. Banach Center Publications, Tome 65 (2004) pp. 151-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc65-0-11/