In other words, its acceleration is normal to the manifold so that the geodesic curvature is zero along the geodesic, and thus the two-point boundary value problem (TPBVP) arises from geodesic differential equations on Riemannian manifold.
g] denote the geodesic curvature of a curve [gamma] at a point P [member of] [gamma] which measures how a curve [gamma] deviates from being a geodesic [24, 30-33].
g] are geodesic torsion, normal curvature and geodesic curvature, respectively.
The following geodesic curvature equalities are satisfied for the parameter curves ([c.
g] is the geodesic curvature of the timelike curve [alpha] on the [([s.
Secondly, we obtain differential equations about in terms of their geodesic curvatures.
Normal and geodesic curvature
of variable lead helix
g] are called the geodesic curvature
, the normal curvature and the geodesic torsion, respectively.
g] (v) is the geodesic curvature of the curve f on [S.
g](s) = -<n'(s), g(s)> are called the normal curvature, the geodesic curvature and the geodesic torsion of [?
g] denote the Gaussian curvature and the geodesic curvature
of M with respect to the metric g.
a curve on a surface, whose geodesic curvature
on each point is zero, is called a geodesic line.