Almost {\alpha}-Paracosymplectic Manifolds

This paper is a complete study of almost {\alpha}-paracosmplectic manifolds. We characterize almost {\alpha}-paracosmplectic manifolds which have para Kaehler leaves. Main curvature identities which are fulfilled by any almost {\alpha}-paracosmplectic manifold are found. We also proved that {\xi} is a harmonic vector field if and only if it is an eigen vector field of the Ricci operator. We locally classify three dimensional almost {\alpha}-para-Kenmotsu manifolds satisfying a certain nullity condition. We show that this condition is invariant under D_{{\gamma},{\beta}}-homothetic deformation. Furthermore, we construct examples of almost {\alpha}-paracosmplectic manifolds satisfying generalized nullity conditions