Some subtleties of Riemannian geometry

 Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences
 101-1 ,Vernadskii Ave., Moscow, 119526, Russia
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Updated December 16,, 2008


It is shown, that the conventional presentation of the Maxwell equations for the electromagnetic field in the Riemannian space-time appears to be problematic. The reason of hesitations is the fact, that a solution of the Maxwell equations in the space-time of Minkowski do not turn into solution of the Maxwell equations in the Riemannian space-time after replacement of Minkowskian world function s_M   by the world function s_R of the Riemannian space-time in the solution.

There is text of the paper in English (ps,pdf) and in Russian (ps, pdf)