Almost alpha-paracosymplectic manifolds

作者：Erken I Kupeli; Dacko P; Murathan C^*

来源：Journal of Geometry and Physics, 2015, 88: 30-51.

DOI：10.1016/j.geomphys.2014.09.011

• Almost paracontact metric manifold
• Almost paracosymplectic manifold
• Almost para-Kenmotsu manifold
• Para-Kaehler manifold

This paper is a complete study of almost alpha-paracosymplectic manifolds. Basic properties of such manifolds are obtained and general curvature identities are proved. The manifolds with para-Kaehler leaves are characterized. It is proved that, for dimensions greater than 3, almost alpha-paracosymplectic manifolds are locally conformal to almost paracosymplectic manifolds and locally D-homothetic to almost para-Kenmotsu manifolds. Furthermore, it is proved that characteristic (Reeb) vector field xi is harmonic on almost alpha-para-Kenmotsu manifold if and only if it is an eigenvector of the Ricci operator. It is showed that almost alpha-para-Kenmotsu (kappa, mu, nu)-space has para-Kaehler leaves. 3-dimensional almost alpha-para-Kenmotsu manifolds are classified. As an application, it is obtained that 3-dimensional almost alpha-para-Kenmotsu manifold is (kappa, mu, nu)-space on an every open and dense subset of the manifold if and only if Reeb vector field is harmonic. Furthermore, examples are constructed.

• 出版日期2015-2