Denote by e(t) := [gamma](t) the unit tangent vector
By using the pseudo orthonormal frame given by (Equation 2) we already computed the energy of tangent vector
T and parallel frame vectors [E.sub.1], [E.sub.2], [E.sub.3] for timelike curve [alpha] [member of] [E.sup.4.sub.1], (Korpinar & Demirkol, 2017).
We can choose this local coordinate system to be the Serret-Frenet frame consisting of the tangent vector
[??](t), the binormal vector [??](t), and the normal vector [??](t) vectors at any point on the curve given by
Based on the differential geometry , the tangent vector
[??] at this point should be
Here d[x.sup.[mu]]/d[lambda] is defined as the tangent vector
fields to the radial null geodesics and [R.sub.[mu][nu]] is the Ricci tensor.
where X is a tangent vector
field on [[summation].sup.n].
A fiber pathway can be considered as a 3D curve, and its local tangent vector
is consistent with the diffusion orientation .
To obtain ([w.sup.(k+1)], [[lambda].sub.k+1]), we must compute the tangent vector
Given a tangent vector
field X, JX is also tangent to S.
The projective tensor [h.sub.ij] = [[bar.g].sub.ij] + [u.sub.i][u.sub.j] is used to project a tangent vector
at a point p in [bar.M] into a spacelike vector orthogonal to u at p.
6 depicts the tangent vector
at the event point earth.
where k is the curvature, s is the arc length such that ds/dt = [absolute value of r'], and e and n are, respectively, the unit tangent vector
and the normal vector at each point of the curve r(t).