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The gravitational field and the source-free electromagnetic field can beunified preliminarily by the equations in the Riemannian geometry, both arecontractions of im and ik, respectively. So it will be equivalent to the Yanggravitational equations. From this we can obtain the Lorentz equations ofmotion, the first system and second source-free system of Maxwell fieldequations. This unification can be included in the gauge theory, and theunified gauge group is GL(2,C), which is just the same as the gauge group ofthe Riemanian manifold.

Unification of Gravitational and Electromagnetic Fields in Riemannian Geometry