标题： 麦克斯韦方程在黎曼时空中的表现，介质中物质方程的几何效应 显示英文标题

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

摘要： 已知在弯曲时空中的（真空）麦克斯韦方程可以视为在平坦时空中的麦克斯韦方程（Mandel'stam L.I., Tamm I.E.），这些方程是在一种有效介质中考虑的，该介质的性质由弯曲模型的度规结构决定。弯曲时空的度规结构为电磁场生成了有效的本构方程，对于任意黎曼时空的一般情况，四个相应的对称张量的形式被明确找到。四个本构张量并非相互独立，它们之间存在一些额外的约束。详细指定了几个简单的例子：给出了各向异性介质（磁性晶体）的几何建模，以及在闵可夫斯基电动力学中运动参考系中的均匀介质的几何建模——后者是通过使用由运动均匀介质的四维速度确定的非对角度规张量实现的。还确定了由常曲率空间几何（洛巴切夫斯基和黎曼模型）产生的有效物质方程。 显示英文摘要

摘要： The known possibility to consider the (vacuum) Maxwell equations in a curved space-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 metrical structure of the curved model is studied. Metrical structure of the curved space-time generates effective constitutive equations for electromagnetic fields, the form of four corresponding symmetrical tensors is found explicitly for general case of an arbitrary Riemannian space - time. Four constitutive tensors are not independent and obey some additional constraints between them. Several simple examples are specified in detail:itis given geometrical modeling of the anisotropic media (magnetic crystals) and the geometrical modeling of a uniform media in moving reference frame in the Minkowsky electrodynamics -- the latter is realized trough the use of a non-diagonal metrical tensor determined by 4-vector velocity of the moving uniform media. Also the effective material equations generated by geometry of space of constant curvature (Lobachevsky and Riemann models) are determined.