Para-CR Structures on almost Paracontact Metric Manifolds

Joanna Wełyczko

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arXiv · 1202.6383

Para-CR Structures on almost Paracontact Metric Manifolds

Joanna Wełyczko

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Abstract

Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and suffcient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that the normal almost paracontact metric manifolds are para-CR. We establish necessary and suffcient conditions for paracontact metric manifolds as well as for almost paracosymplectic manifolds to be para-CR. We find also basic curvature identities for para-CR paracontact metric manifolds and study their consequences. Among others, we prove that any para-CR paracontact metric manifold of constant sectional curvature and of dimension greather than tree must be para-Sasakian and its curvature equal to minus one. The last assertion do not hold in dimension tree. Moreover, we show that a conformally flat para-Sasakian manifold is of constant sectional curvature equal to minus one. New classes of examples of para-CR manifolds are established.

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Joanna Wełyczko. 2012-02-28. Para-CR Structures on almost Paracontact Metric Manifolds. https://arxiv.org/abs/1202.6383

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