We study Legendre and slant curves for Bianchi-Cartan-Vranceanu metrics. These curves are characterized through the scalar product between the normal at the curve and the vertical vector field and in the helix case they have a proper (non-harmonic) mean curvature vector field. The general expression of the curvature and torsion of these curves and the associated Lancret invariant (for the slant case) are computed as well as the corresponding variant for some particular cases. The slant (particularly...

The object of the present paper is to study some types of semisymmetry conditions on two classes of almost Kenmotsu manifolds. It is shown that a $(k,\mu )$-almost Kenmotsu manifold satisfying the curvature condition $Q·R=0$ is locally isometric to the hyperbolic space ${ℍ}^{2n+1}(-1)$. Also in $(k,\mu )$-almost Kenmotsu manifolds the following conditions: (1) local symmetry $(\nabla R=0)$, (2) semisymmetry $(R·R=0)$, (3) $Q(S,R)=0$, (4) $R·R=Q(S,R)$, (5) locally isometric to the hyperbolic space ${ℍ}^{2n+1}(-1)$ are equivalent. Further, it is proved that a ${(k,\mu )}^{\text{'}}$-almost Kenmotsu manifold satisfying...

We give a complete classification of surfaces with parallel second fundamental form in 3-dimensional Bianchi-Cartan-Vranceanu spaces.