Sequential natural mates of Frenet curves in Euclidean 3-space

<abstract><p>In this paper, we give some characterizations of Frenet curves in 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. We compute the Frenet equations and Frenet elements of these curves. We also obtain the curvatures of non-geodesic Frenet curves on 3-dimensional $ \delta $-Lorentzian trans-Sasakian manifolds. Finally, we give some results for these curves.</p></abstract>

Download Full-text

On curves in 3-dimensional normal almost contact metric manifolds

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887821500043 ◽

2020 ◽

Vol 18 (01) ◽

pp. 2150004

Author(s):

Abdullah Yıldırım

Keyword(s):

Contact Manifolds ◽

3 Dimensional ◽

And Topology ◽

Contact Metric Manifolds ◽

Almost Contact Metric ◽

Almost Contact Metric Manifolds ◽

Frenet Curves

The characterization of curves plays an important role in both geometry and topology of almost contact manifolds. Olszak found the equation [Formula: see text] on normal almost contact manifolds. The pair [Formula: see text] denotes the type of these manifolds. In this study, we obtained the curvatures of non-geodesic Frenet curves on [Formula: see text]-dimensional normal almost contact manifolds without neglecting [Formula: see text] and [Formula: see text], and provided the results of their characterization. We exemplified these results with examples.

Download Full-text

The complete classification of a class of conformally flat Lorentzian hypersurfaces in ℝ14

International Journal of Mathematics ◽

10.1142/s0129167x17500926 ◽

2017 ◽

Vol 28 (13) ◽

pp. 1750092

Author(s):

Zhenxiao Xie ◽

Changping Wang ◽

Xiaozhen Wang

Keyword(s):

Three Dimensional ◽

Complete Classification ◽

Conformally Flat ◽

Space Forms ◽

Lorentzian Space ◽

Lorentzian Metric ◽

Cone Model ◽

Shape Operators ◽

Frenet Curves

A three-dimensional Lorentzian hypersurface [Formula: see text] is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, this property is preserved under the conformal transformation of [Formula: see text]. In this paper, using the projective light-cone model, we give a complete classification of those ones whose shape operators have two distinct real eigenvalues and cannot be diagonalizable. These hypersurfaces are conformal equivalent to cones, cylinders, or rotational hypersurfaces generated by B-scrolls (over null Frenet curves) in three-dimensional Lorentzian space forms.

Download Full-text