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 $\alpha -$cosymplectic $(\kappa ,\mu )-$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 umbilical), ii) $M$ has a constant $\xi -$sectional curvature (under this condition the integral manifold of the distribution $D$ is totally geodesic (or totally umbilical) or the manifold is isometric to sphere $S^{2n+1}\left(\sqrt{c}\right)$ of radius $\frac{1}{\sqrt{c}}$), iii) $M$ an almost $\alpha -$cosymplectic $(\kappa ,\mu )-$spaces ( in this case the manifold has constant curvature, or the integral manifold of the distribution $D$ is totally geodesic(or totally umbilical) or $U$ is an eigenvector of $h).$

Keywords

• Almost $\alpha$-cosymplectic $(\kappa,\mu)$-spaces
• $\alpha$- cosymplectic manifold
• Hpcv field

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