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Journal of Lie Theory 17 (2007), No. 3, 563--581
Copyright Heldermann Verlag 2007
Reduction Theorems for Manifolds with Degenerate 2-Form
Luigia Di Terlizzi
Dip. di Matematica, Via Orabona 4, 70125 Bari, Italy
terlizzi@dm.uniba.it
Jerzy J. Konderak †
Dip. di Matematica, Via Orabona 4, 70125 Bari, Italy
We consider a manifold with a 2-form and an action of a Lie group on the manifold which preserves the form. We define a momentum map and study its properties in this context. In particular we obtain a reduction theorem. Then we apply our reduction theorem to a certain generalization of the contact metric manifolds.
Keywords: Degenerate symplectic form, momentum map, symplectic reduction, K,C,S-structures, generalized contact metric structure.
MSC: 53D20, 53C15, 53C25
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