Abstract
The differential geometry of curves on a hypersphere in the Euclidean space reflects instantaneous properties of spherecal motion. In this work, we give some results for differential geometry of spacelike curves in 3-dimensional de-Sitter space. Also, we study the Frenet reference frame, the Frenet equations, and the geodesic curvature and torsion functions to analyze and characterize the shape of the curves in 3-dimensional de-Sitter space.
Highlights
IntroductionXx , y14 denote y1, y2 , y3, y4 , 14 , [1]. is defined by the 3-dimensional unitary de-Sitter space, that is, 13 14 is the hyperquadric,
We give some results for differential geometry of spacelike curves in 3-dimensional de-Sitter space
We study the Frenet reference frame, the Frenet equations, and the geodesic curvature and torsion functions to analyze and characterize the shape of the curves in 3-dimensional de-Sitter space
Summary
Xx , y14 denote y1, y2 , y3, y4 , 14 , [1]. is defined by the 3-dimensional unitary de-Sitter space, that is, 13 14 is the hyperquadric,. Xx , y14 denote y1, y2 , y3, y4 , 14 , [1]. Is defined by the 3-dimensional unitary de-Sitter space, that is, 13 14 is the hyperquadric,. Y1 y2 y3 y4 z1 z2 z3 z4 where e1, e2 , e3, e4 is the canonical basis of 14 , [2]. Vector u ux ,uy ,uz along the axis of the rotation and a rotation angle. The Euler parameters of the rotation defined in terms of u and can be used to prescribe a mapping of this rotation to a point in a higher dimensional space [4,5,6]. Let u ux ,uy ,uz denote a timelike rotation axis. AYYILDIZ we will use the exterior algebra of multivectors
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