Invariant submanifolds and properCR foliations on a para-coKählerian manifold with concircular structure vector field

Abstract

After recalling the basic properties of para-coKahlerian manifolds\(\tilde M\) with concircular structure vector field ξ, the infinitesimal auto morphismsX of the structure 1-form\(\tilde \eta \) are considered. One of the results is that the Lie derivative of all powers of the structure 2-form\(\tilde \Omega ,\) i.e.\(\mathcal{L}x\tilde \Omega ^p ;p = 1,...,m,\) is exterior recurrent. Further two types of horizontal distributionsDn which are normal to ξ. IfDt (resp.Dn) is involutive, the corresponding leafMt (resp.Mn) is a minimal submanifold of\(\tilde M\). FurtherMn is a symplectic submanifold and ξ is an umbilical normal section ofMn.