Space-Like Slant Curves in Three-Dimensional Normal Almost Paracontact Geometry

The aim of this paper is to study (spacelike) slant curves of three-dimensional normal almost paracontact manifolds as natural generalization of Legendre curves. Such a curve is characterized by means of the scalar product between its normal vector field and the characteristic vector field of the ambient space. In the particular case of a helix, we show that it has a proper (non-harmonic) mean curvature vector field. The general expressions of the curvature and torsion of these curves and the associated Lancret invariant are computed as well as the corresponding variants for the quasi-para-Sasakian case. Two examples (one of us and one of Joanna Wełyczko) are discussed for a normal not quasi-para-Sasakian 3-manifold.