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Riemann and sectional curvatures of magnetic twisted flux tubes in Riemannianmanifold are computed to investigate the stability of the plasma astrophysicaltubes. The geodesic equations are used to show that in the case of thickmagnetic tubes, the curvature of planar (Frenet torsion-free) tubes have theeffect ct of damping the flow speed along the tube. Stability of geodesic flowsin the Riemannian twisted thin tubes (almost filaments), against constantradial perturbations is investigated by using the method of negative sectionalcurvature for unstable flows. No special form of the flow like Beltrami flowsis admitted, and the proof is general for the case of thin magnetic flux tubes.In the magnetic equilibrium state, the twist of the tube is shown to displayalso a damping effect on the toroidal velocity of the plasma flow. It is foundthat for positive perturbations and angular speed of the flow, instability isachieved, since the sectional Ricci curvature of the magnetic twisted tubemetric is negative. Solar flare production may appear from these geometricalinstabilities of the twisted solar loops.

Geodesic plasma flows instabilities of Riemann twisted solar loops