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The known possibility to consider the (vacuum) Maxwell equations in a curvedspace-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.)taken in an effective media the properties of which are determined by metricalstructure of the curved model is studied. Metrical structure of the curvedspace-time generates effective constitutive equations for electromagneticfields, the form of four corresponding symmetrical tensors is found explicitlyfor general case of an arbitrary Riemannian space - time. Four constitutivetensors are not independent and obey some additional constraints between them.Several simple examples are specified in detail:itis given geometrical modelingof the anisotropic media (magnetic crystals) and the geometrical modeling of auniform media in moving reference frame in the Minkowsky electrodynamics -- thelatter is realized trough the use of a non-diagonal metrical tensor determinedby 4-vector velocity of the moving uniform media. Also the effective materialequations generated by geometry of space of constant curvature (Lobachevsky andRiemann models) are determined.

Maxwell equations in Riemannian space-time, geometry effect on material equations in media