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

Authors : Mustafa Yildirim, Nesip Aktan

Pages : 35-41

Doi:10.33401/fujma.1153224

View : 18 | Download : 9

Publication Date : 2023-03-29

Article Type : Research

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) U U is pointwise collinear with ξ ξ ( in this case, the integral manifold of the distribution D D is totally geodesic, or totally umbilical), ii) M M has a constant ξ − ξ− sectional curvature (under this condition the integral manifold of the distribution D D is totally geodesic (or totally umbilical) or the manifold is isometric to sphere S 2 n + 1 ( √ c ) S2n+1(c) of radius 1 √ c 1c ), iii) M M 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 D D is totally geodesic(or totally umbilical) or U U is an eigenvector of h ) . h).
Keywords : Almost $\\alpha$-cosymplectic $(\\kappa, \\mu)$-spaces, $\\alpha$- cosymplectic manifold, Hpcv field