Slant Curves in 3-dimensional Normal Almost Contact Geometry

Abstract

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Slant and Legendre curves in Bianchi-Cartan-Vranceanu geometry

“…Some results already known from [8] and [12] are reobtained with particular choices of the parameters; but to the best of our knowledge, until now there have been no general expressions for Legendre curves in Nil 3 nor for their curvature and torsion in S 3 .…”

“…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.…”

“…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. Another feature of the present paper, as compared with [8], is that here we do not use the structural tensor field ϕ of (1, 1)-type, which is a main tool in almost contact geometry.…”

SLANT CURVES IN 3-DIMENSIONAL ALMOST f-KENMOTSU MANIFOLDS

“…Cȃlin and Crasmareanu [5] studied slant curves in 3-dimensional normal almost contact geometry. Moreover, Cȃlin, Crasmareanu and Munteanu [6] studied slant curves with proper mean curvature vector field in three-dimensional f -Kenmotsu manifolds.…”

Mechanical Equations on Slant Curves in 3-dimensional Normal Almost Paracontact Metric Manifolds

“…Calin et al studied slant curves of threedimensional f-Kenmotsu manifolds [4]. Calin and Crasmareanu examined slant curves of threedimensional normal almost contact manifolds as natural generalization of Legendre curves [5]. Kasap and Tekkoyun found Lagrangian and Hamiltonian formalism for mechanical systems using para/pseudo-Kähler manifolds [6].…”