Two Special Types of Curves in Lorentzian α-Sasakian 3-Manifolds
Author:
Chen Xiawei1ORCID,
Liu Haiming1ORCID
Affiliation:
1. School of Mathematics, Mudanjiang Normal University, Mudanjiang 157011, China
Abstract
In this paper, we focus on the research and analysis of the geometric properties and symmetry of slant curves and contact magnetic curves in Lorentzian α-Sasakian 3-manifolds. To do this, we define the notion of Lorentzian cross product. From the perspectives of the Legendre and non-geodesic curves, we found the ratio relationship between the curvature and torsion of the slant curve and contact magnetic curve in the Lorentzian α-Sasakian 3-manifolds. Moreover, we utilized the property of the contact magnetic curve to characterize the manifold as Lorentzian α-Sasakian and to find the slant curve type of the Frenet contact magnetic curve. Furthermore, we found an example to verify the geometric properties of the slant curve and contact magnetic curve in the Lorentzian α-Sasakian 3-manifolds.
Funder
Special Fund for Scientific and Technological Innovation of Graduate Students in Mudanjiang Normal University
Project of Science and Technology of Mudanjiang Normal University
Natural Science Foundation of Heilongjiang Province of China
Reform and Development Foundation for Local Colleges and Universities of the Central Government
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference37 articles.
1. A study of conformal η-Einstein solitons on trans-Sasakian 3-manifold;Li;J. Nonlinear Math. Phy.,2022
2. On Lorentzian α-Sasakian manifolds;Yildiz;Kyungpook Math. J.,2005
3. A class of Lorentzian α-Sasakian manifolds;Yildiz;Kyungpook Math. J.,2009
4. Ricci solitons in Lorentzian α-Sasakian manifolds;Bagewadi;Acta Math. Acad. Paedagog. Nyhaázi. (NS),2012
5. Lorentzian approximations for a Lorentzian α-Sasakian manifold and Gauss-Bonnet theorems;Liu;AIMS Math.,2023