A+ CATEGORY SCIENTIFIC UNIT

Special Lagrangian linear subspaces in product symplectic space

Volume 65 / 2004

Małgorzata Mikosz Banach Center Publications 65 (2004), 151-156 MSC: Primary 53D12, 51A50; Secondary 15A03, 53C38. DOI: 10.4064/bc65-0-11

Abstract

The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism $f:(\mathbb R^{2n},\sigma =\sum_{i=1}^n dx_i\wedge dy_i)\rightarrow (\mathbb R^{2n},\sigma)$ to be a special Lagrangian linear subspace in $(\mathbb R^{2n}\times \mathbb R^{2n},\omega=\pi^*_2\sigma -\pi^*_1\sigma)$. This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian $S\Lambda_{2n}\simeq {SU(2n)/SO(2n)}$ is defined.

Authors

  • Małgorzata MikoszFaculty of Mathematics and Information Science
    Warsaw University of Technology
    Plac Politechniki 1
    00-661 Warszawa, Poland
    e-mail

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