Biswas, Indranil ; Raina, A. K.
(2008)
*Symplectic connections on a Riemann surface and holomorphic immersions in the Lagrangian homogeneous space*
Journal of Geometry and Physics, 58
(10).
pp. 1417-1428.
ISSN 0393-0440

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S03930...

Related URL: http://dx.doi.org/10.1016/j.geomphys.2008.06.001

## Abstract

Let Gr_{L}⊂ Gr(n, V) be the space of all Lagrangian subspaces C^{2n} of equipped with the standard symplectic form. Let X^{~} be a universal cover of a compact connected Riemann surface X. We consider all immersions f : X^{~}→ Gr_{L} satisfying the following two conditions: (1) the map f is equivariant with respect to some homomorphism into Sp(2n,C) of the Galois group of the covering X^{~} → X, and (2) the symmetric bilinear form on the pullback, to X, of the tautological vector bundle over Gr_{L} is fiberwise nondegenerate. Two such maps are called equivalent if they differ by the action of some fixed element of Sp(2n,C). We prove that the equivalence classes of all such maps are bijectively parametrized by pairs of the form (P, (F,∇ ) where P is a projective structure on X and (F,∇ ) is an equivalence class of flat O(n,C)-connection on X. Two flat O(n,C)-bundles are equivalent if the corresponding flat PO(n,C)-bundles are isomorphic.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Symplectic Connection; Differential Operator; Lagrangian Subspace |

ID Code: | 3646 |

Deposited On: | 18 Oct 2010 10:10 |

Last Modified: | 18 Oct 2010 10:10 |

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