Pointwise Slant Curves in Quasi-paraSasakian 3-Manifolds

2020 ◽  
Vol 17 (4) ◽  
Author(s):  
K. Sood ◽  
K. Srivastava ◽  
S. K. Srivastava
Keyword(s):  
Slant Curves

scholarly journals N-Legendre and N-slant curves in the unit tangent bundle of Minkowski surfaces

2017 ◽  
Vol 11 (01) ◽  
pp. 1850008 ◽  
Author(s):  
Murat Bekar ◽  
Fouzi Hathout ◽  
Yusuf Yayli
Keyword(s):  
Tangent Bundle ◽  
Inner Product ◽  
Normal Vector ◽  
Sasaki Metric ◽  
Reeb Vector ◽  
Nonzero Constant ◽  
Unit Tangent Bundle ◽  
Slant Curves

Let [Formula: see text] be a unit tangent bundle of Minkowski surface [Formula: see text] endowed with the pseudo-Riemannian induced Sasaki metric. In this present paper, we studied the N-Legendre and N-slant curves in which the inner product of its normal vector and Reeb vector is zero and nonzero constant, respectively, in [Formula: see text] and several important characterizations of these curves are given.

scholarly journals On slant curves in Sasakian 3-manifolds

2006 ◽  
Vol 74 (3) ◽  
pp. 359-367 ◽  
Author(s):  
Jong Taek Cho ◽  
Jun-Ichi Inoguchi ◽  
Ji-eun Lee
Keyword(s):  
Classical Theorem ◽  
Curvature And Torsion ◽  
Constant Slope ◽  
Slant Curves

A classical theorem by Lancret says that a curve in Euclidean 3-space is of constant slope if and only if its ratio of curvature and torsion is constant. In this paper we study Lancret type problems for curves in Sasakian 3-manifolds.

scholarly journals Slant Curves in Contact Lorentzian Manifolds with CR Structures

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 46
Author(s):  
Ji-Eun Lee
Keyword(s):  
Vector Fields ◽  
Lorentzian Manifold ◽  
Space Forms ◽  
Lorentzian Space ◽  
Geodesic Vector ◽  
Magnetic Curve ◽  
Cr Structures ◽  
Necessary And Sufficient ◽  
Jacobi Equations ◽  
Slant Curves

In this paper, we first find the properties of the generalized Tanaka–Webster connection in a contact Lorentzian manifold. Next, we find that a necessary and sufficient condition for the ∇ ^ -geodesic is a magnetic curve (for ∇) along slant curves. Finally, we prove that when c ≤ 0 , there does not exist a non-geodesic slant Frenet curve satisfying the ∇ ^ -Jacobi equations for the ∇ ^ -geodesic vector fields in M. Thus, we construct the explicit parametric equations of pseudo-Hermitian pseudo-helices in Lorentzian space forms M 1 3 ( H ^ ) for H ^ = 2 c > 0 .

scholarly journals Slant Curves and Contact Magnetic Curves in Sasakian Lorentzian 3-Manifolds

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 784 ◽  
Author(s):  
Ji-Eun Lee
Keyword(s):  
Three Dimensional ◽  
Lorentzian Manifold ◽  
Cross Product ◽  
Slant Curve ◽  
Magnetic Curve ◽  
Three Space ◽  
Slant Curves

In this article, we define Lorentzian cross product in a three-dimensional almost contact Lorentzian manifold. Using a Lorentzian cross product, we prove that the ratio of κ and τ − 1 is constant along a Frenet slant curve in a Sasakian Lorentzian three-manifold. Moreover, we prove that γ is a slant curve if and only if M is Sasakian for a contact magnetic curve γ in contact Lorentzian three-manifold M. As an example, we find contact magnetic curves in Lorentzian Heisenberg three-space.

Slant Curve in Lorentzian BCV Spaces

2020 ◽  
Vol 56 ◽  
pp. 67-85
Author(s):  
Abdullah Yildirim ◽  
Keyword(s):  
Directional Derivative ◽  
Lorentzian Manifolds ◽  
Slant Curve ◽  
Slant Curves

The aim of this study is to examine the slant curves in Lorentzian manifolds with BCV (Bianchi-Cartan-Vranceanu) metrics. A practical form of the directional derivative in the presence of the BCV metrics is presented. Moreover, some theorems for slant curves in Lorentzian BCV manifolds are proved.

scholarly journals Slant Curves in the Unit Tangent Bundles of Surfaces

ISRN Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Zhong Hua Hou ◽  
Lei Sun
Keyword(s):  
Vector Field ◽  
Tangent Bundle ◽  
Unit Vector ◽  
Sasaki Metric ◽  
Geometric Properties ◽  
Unit Vector Field ◽  
Unit Tangent Bundle ◽  
Tangent Bundles ◽  
Slant Curves

Let (M,g) be a surface and let (U(TM),G) be the unit tangent bundle of M endowed with the Sasaki metric. We know that any curve Γ(s) in U(TM) consist of a curve γ(s) in M and as unit vector field X(s) along γ(s). In this paper we study the geometric properties γ(s) and X(s) satisfying when Γ(s) is a slant geodesic.

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