Journal of Lie Theory 16 (2006), No. 3, 471--482
Copyright Heldermann Verlag 2006
Reduction Theorems for a Certain Generalization of Contact Metric Manifolds
Luigia Di Terlizzi
Dip. di Matematica, Università di Bari, Via Orabona 4, 70125 Bari, Italy
terlizzi@dm.uniba.it
Jerzy J. Konderak
Dip. di Matematica, Università di Bari, Via Orabona 4, 70125 Bari, Italy
konderak@dm.uniba.it
We consider a Riemannian manifold with a compatible f-structure which admits a parallelizable kernel. With some additional integrability conditions it is called an (almost) S-manifold, which is a natural generalization of a contact metric and a Sasakian manifold. Then we consider an action of a Lie group preserving the given structures. In such a context we define a momentum map and prove some reduction theorems.
Keywords: Contact metric manifold, momentum map, contact reduction, generalized contact metric manifold, f-structure.
MSC: 53D10, 53D20, 53C15, 53C25
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