Holomorphically planar conformal vector fields on almost alpha-cosymplectic (k,m)-spaces

Abstract

The aim of the present paper is to study holomorphically planar conformal vector fields(HPCV) on almost alpha-cosymplectic (k,m)-spaces. This is done assuming various conditions such as i) U is pointwise collinear with xi ( in this case the integral manifold of the distribution D is totally geodesic or totally umbilic), ii) M has a constant xi-sectional curvature (under this condition the integral manifold of the distribution D is totally geodesic (or totally umbilic) or the manifold is isometric to sphere S2n+1(pc) of radius 1 pc ), iii) M an almost alpha-cosymplectic (k,m)-spaces ( in this case the manifold is constant negative curvature or the integral manifold of the distribution D is totally geodesic(or totally umbilic) or U is an eigenvector of h).