-dimensional spacelike parallel -equidistant ruled surfaces in the Minkowski space .
On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat.
The object of the present paper is to study -Ricci solitons on -Einstein -manifolds. It is shown that if is a recurrent torse forming -Ricci soliton on an -Einstein -manifold then is (i) concurrent and (ii) Killing vector field.
In this paper we study vector fields in Riemannian spaces, which satisfy , , We investigate the properties of these fields and the conditions of their coexistence with concircular vector fields. It is shown that in Riemannian spaces, noncollinear concircular and -vector fields cannot exist simultaneously. It was found that Riemannian spaces with -vector fields of constant length have constant scalar curvature. The conditions for the existence of -vector fields in symmetric spaces are given....