Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 465-479 (2004)

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A symplectic reduction for pseudo-Riemannian manifolds with compatible almost product structures

Jerzy J. Konderak

Dipartimento di Matematica Universit{à} di Bari, Via Orabona 4, 70125 Bari, Italy, e-mail:

Abstract: We consider a manifold $M$ with a pseudo-Riemannian metric $g$ and an almost product structure $P$ such that $g(P(X),P(Y))=-g(X,Y)$. We suppose that the almost product structure $P$ is parallel with respect to the Levi-Civita connection of $g$. These induce a natural symplectic structure on $M$. We consider an isometric action of a Lie group $G$ on $M$ preserving the pseudo-Riemannian metric and the almost product structure $P$. Then we prove a symplectic reduction theorem for such manifolds. We obtain a reduced manifold with a pseudo-Riemannian metric and a parallel almost product structure.

Keywords: symplectic manifold, almost product structure, symplectic reduction, para-Kähler manifold, Lagrangian foliation

Classification (MSC2000): 53D20, 53C15

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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.

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