Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

Characterization of Legendre curves in quasi-Sasakian pseudo-metric 3-manifolds

“…If υ is an integral curve of the contact distribution D = Ker η, equivalently, η(υ ) = 0 then we say that υ is a Legendre curve in M. These curves have been intensively studied by several authors (see [1,2,3,4,10,12,14]).…”

“…Legendre curves in Q3 Let υ be a non-geodesic Legendre curve in a quasi-Sasakian pseudo-metric 3-manifold Q 3 . Then by the virtue of proposition 3.1, curvature and torsion of υ are given by κ = ϑ, τ = |α|,(3.18)where ϑ = g (∇ υ υ , ϕυ ) > 0 and α being the same as in(2.5).…”

On Slant Curves with pseudo-Hermitian $C$-parallel Mean Curvature Vector Fields

“…C-parallel and C-proper slant curves in trans-Sasakian manifolds were studied in [15], by Güvenç and the present author. On the other hand, slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry were studied by Cȃlin and Crasmareanu in [6]. Slant curves in normal almost contact geometry were studied in [5].…”