Biharmonic curves on \textit{LP}-Sasakian manifolds
Sad{\i}k Kele\c{s}, Selcen Y\"uksel Perkta\c{s}, Erol K{\i}l{\i}\c{c}
TL;DR
This paper characterizes proper biharmonic curves in specific 4-dimensional LP-Sasakian manifolds and explores their properties in the Lorentzian sphere, contributing to the understanding of biharmonic curves in Lorentzian geometry.
Contribution
It provides necessary and sufficient conditions for proper biharmonic curves in conformally flat, quasi conformally flat, and conformally symmetric LP-Sasakian manifolds, including Lorentzian spheres.
Findings
Characterization of proper biharmonic curves in LP-Sasakian manifolds
Conditions for spacelike and timelike curves to be biharmonic
Analysis of biharmonic curves in Lorentzian sphere S^4_1
Abstract
In this paper we give necessary and sufficient conditions for spacelike and timelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional \textit{LP}-Sasakian manifold to be proper biharmonic. Also, we investigate proper biharmonic curves in the Lorentzian sphere .
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology