  In this work we have obtained the exact quantum expressions for the
compenents of the Levi Cevita connection, the Ricci tensor and the scalar
curvature, generalizing those of \cite{CTZX08} for a spherical surface via the
noncommutative Moyal star product, and we have established equations describing
quantum effect on the geodesic flow equation or auto parallel fields equations.
These later are solved for the zero and the first orders of the quantum
parameter $\alpha$ when $y$-symmetry is assumed. We expressed the general
system of equations in terms of Fourier modes indexed by the integer
$p=1,2,...,\infty$ to understand the interdependence of $y$ modes oscillations.
