  Two examples of the use of differential geometry in plasma physics are given:
The first is the computation and solution of the constraint equations obtained
from the Riemann metric isometry of the twisted flux tube. In this case a
constraint between the Frenet torsion and curvature is obtained for
inhomogeneous helical magnetic flux tube axis. In the second one, geometrical
and topological constraints on the current-carrying solar loops are obtained by
assuming that the plasma filament is stable. This is analogous to early
computations by Liley [(Plasma Physics (1964)] in the case of hydromagnetic
equilibria of magnetic surfaces. It is shown that exists a relationship between
the ratio of the current components along and cross the plasma filament and the
Frenet torsion and curvature. The computations are performed for the helical
plasma filaments where torsion and curvature are proportional. The constraints
imposed on the electric currents by the energy stability condition are used to
solve the remaining magnetohydrodynamical (MHD) equations which in turn allows
us to compute magnetic helicity and from them the twist and writhe topological
numbers. Magnetic energy is also computed from the solutions of MHD equations.
