In this article, normal paracontact metric space forms are investigated on W_0-curvature tensor. Characterizations of obtained Special curvature conditions established with the help Riemann, Ricci, concircular tensors discussed With these conditions, important characterizations obtained.

In this paper, we determine necessary and sufficient conditions for a non-Frenet Legendre curve to be $f$-harmonic, $f$-biharmonic, bi-$f$-harmonic, biminimal $f$-biminimal in three-dimensional normal almost paracontact metric manifold. Besides, obtain some nonexistence theorems.

Two correlated Schouten–van Kampen affine connections on an almost paracontact paracomplex Riemannian manifold are introduced and investigated. The considered manifolds characterized by virtue of the presented non-symmetric connections. Curvature properties studied obtained. A family examples a Lie group given in confirmation obtained results.

In the last decade, contact, almost contact, paracontact cosymplectic, and conformal cosymplectic manifolds carrying κ > 1 structure vector fields ξ have been studied by many authors, e.g. [2], [7], [11], [15]. In the present paper we consider a (2m + 2)-dimensional Riemannian manifold carrying two structure vector fields ξ (r ∈ {2m+1, 2m+2}), a (1, 1)-tensor field Φ, and a structure 2 form Ω o...