  The ideal magnetohydrodynamic theorem on the conservation of the magnetic
connections between plasma elements is extended to non-ideal relativistic
plasmas in curved spacetime. The existence of generalized magnetofluid
connections that are preserved by the plasma dynamics is formalized by means of
a covariant connection equation that includes different non-ideal effects.
These generalized connections are constituted by 2-dimensional hypersurfaces,
which are linked to an antisymmetric tensor field that unifies the
electromagnetic and fluid fields. They can be interpreted in terms of
generalized magnetofluid vorticity field lines by considering a 3+1 foliation
of spacetime and a time resetting projection that compensates for the loss of
simultaneity in different reference frames between spatially separated events.
The worldsheets of the generalized magnetofluid vorticity field lines play a
fundamental role in the plasma dynamics by prohibiting evolutions that do not
preserve the magnetofluid connectivity.
