Trigonometric laws on Lorentzian sphere S 1 2

1985 ◽  
Vol 24 (1) ◽  
pp. 6-13 ◽  
Author(s):  
Dzan Jin Jee
Keyword(s):  
Lorentzian Sphere

scholarly journals Differential representation of the Lorentzian spherical timelike curves by using bishop frame

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2037-2043
Author(s):  
Okullu Balki ◽  
Huseyin Kocayigit
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Timelike Curve ◽  
Position Vector ◽  
Order Linear Differential Equation ◽  
Third Order ◽  
Order Linear ◽  
Bishop Frame ◽  
Lorentzian Sphere ◽  
Linear Differential

In this study, we will give the differential representation of the Lorentzian spherical timelike curves according to Bishop frame and we obtain a third-order linear differential equation which represents the position vector of a timelike curve lying on a Lorentzian sphere.

scholarly journals f−BIHARMONIC CURVES WITH TIMELIKE NORMAL VECTOR ON LORENTZIAN SPHERE

2020 ◽  
pp. 311
Author(s):  
Bilal Eftal Acet
Keyword(s):  
Critical Points ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Normal Vector ◽  
Conformally Flat ◽  
Lorentzian Sphere ◽  
Necessary And Sufficient ◽  
Biharmonic Curves

In this paper, we study $f-$biharmonic curves as the critical points of the $f-$bienergy functional $E_{2}(\psi )=\int_{M}f\mid \tau (\psi )^{2}\mid \vartheta _{g}$, on a Lorentzian para-Sasakian manifold $M$. We give necessary and sufficient conditions for a curve such that has a timelike principal normal vector on lying a $4$-dimensional conformally flat, quasi-conformally flat and conformally symmetric Lorentzian para-Sasakian manifold to be an $f-$biharmonic curve. Moreover, we introduce proper $f-$biharmonic curves on the Lorentzian sphere $S_{1}^{4}.$

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