On the characterization of spherical curves in 3-dimensional Sasakian spaces

Abstract

In this paper, we give the spherical characterization of a regular curve in 3-dimensional Sasakian space. Furthermore the differential equation which expresses the mentioned characterization is solved.

On Classifications of Normal and Osculating Curves in 3-dimensional Sasakian Space

“…In this paper, the notations and concepts are used from the literature [5,6,7]. If a (2n+1)-dimensional differentiable manifold M carries a global differential 1-form η such that…”

“…A (2n + 1) −dimensional manifold M is said to be a Sasakian manifold if it is endowed with a normal contact metric structure (φ, ξ, η, g, ε) . It is well known that M is a Sasakian structure if and only if [4,5,7] (…”

“…Let M be a 3-dimensional manifold endowed with the contact metric structure (φ, ξ, η, g, ε) then M is a Sasakian manifold if and only if the torsion of its Legendre curves is ε. Let γ be an arc-length parametrized curve on M, then the Frenet euations of γ can be given partially as follows [3,4,7].…”

Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

“…1) the rôle of Legendre curves in almost contact geometry is remarkable and wellknown; in [4] the reader finds an excellent survey on these curves, 2) although the literature on Legendre curves is rich ( [3], [5], [7], [16], [20], [24], [25]), slant curves have been studied until now only for the Sasakian geometry in [12], for the contact pseudo-Hermitian geometry in [14], for the f -Kenmotsu geometry in [10], in normal almost contact geometry in [8] and for warped products in [9]. Although some Bianchi-Cartan-Vranceanu metrics are almost contact metrics we prefer in the present work a unified treatment in order to emphasize the common properties of these metrics.…”

Differential representation of the Lorentzian spherical timelike curves by using bishop frame

“…Ayyildiz et al [9] presented the differential equation that is characterizing the dual Lorentzian spherical curves and then gave an explicit solution of this differential equation in 2007. Camci et al [10] studied with regular curves in 3-D Sasakian space and gave the spherical characterizations of them. Furthermore, the differential equation which expresses the S2038 THERMAL SCIENCE: Year 2019, Vol.…”