On almost cosymplectic $(\kappa,\mu,\nu)$-spaces
Volume 69 / 2005
Abstract
An almost cosymplectic $(\kappa,\mu,\nu)$-space is by definition an almost cosymplectic manifold whose structure tensor fields $\varphi$, $\xi$, $\eta$, $g$ satisfy a certain special curvature condition (see formula (eq1b)). This condition is invariant with respect to the so-called $\mathcal D$-homothetic transformations of almost cosymplectic structures. For such manifolds, the tensor fields $\varphi$, $h$ $(=(1/2)\mathcal L_{\xi}\varphi)$, $A$ $(=-\nabla\xi)$ fulfill a certain system of differential equations. It is proved that the leaves of the canonical foliation of an almost cosymplectic $(\kappa,\mu,\nu)$-space with $\kappa<0$ are locally flat Kählerian manifolds. A local characterization of such manifolds is established up to a $\mathcal D$-homothetic transformation of the almost cosymplectic structures.
