Holomorphically Planar Conformal Vector Field On Almost $\alpha $-Cosymplectic $(\kappa ,\mu )-$ Spaces

Abstract

The aim of the present paper is to study holomorphically planar conformal vector (HPCV) fields on almost α−α−cosymplectic (κ,μ)−(κ,μ)−spaces. This is done assuming various conditions such as i) UU is pointwise collinear with ξξ ( in this case, the integral manifold of the distribution DD is totally geodesic, or totally umbilical), ii) MM has a constant ξ−ξ−sectional curvature (under this condition the integral manifold of the distribution DD is totally geodesic (or totally umbilical) or the manifold is isometric to sphere S2n+1(√c)S2n+1(c) of radius 1√c1c), iii) MM an almost α−α−cosymplectic (κ,μ)−(κ,μ)−spaces ( in this case the manifold has constant curvature, or the integral manifold of the distribution DD is totally geodesic(or totally umbilical) or UU is an eigenvector of h).h).