黎曼时空中的麦克斯韦方程组，介质中物质方程的几何效应
Maxwell equations in Riemannian space-time, geometry effect on material equations in media
摘要：
将弯曲时空中的（真空）麦克斯韦方程组视为平坦时空中的麦克斯韦方程组的已知可能性（Mandel'Wellington L.I.，Tamm I.E.）研究了由弯曲模型的度量结构决定的有效介质中的非线性问题。弯曲时空的度规结构产生了有效的电磁场本构方程，对于任意黎曼时空的一般情况，明确地找到了四个相应的对称张量的形式。四个本构张量不是相互独立的，它们之间有一些附加的约束。文中详细列举了几个简单的例子：给出了各向异性介质（磁性晶体）的几何模型和运动参考系中均匀介质的几何模型--后者是通过使用由运动均匀介质的四矢量速度确定的非对角度量张量来实现的。确定了由常曲率空间几何（罗巴切夫斯基模型和黎曼模型）产生的有效材料方程。
英文摘要：
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.
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