Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations

Details Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations

2008-05-29

arxiv.org/abs/0805.4479v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

10.1142/S0217751X09042967

In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower dimensional metric is independent of reduced dimensions the counterpart of the symmetric extrinsic curvature is proportional to the antisymmetric Kaluza-Klein gauge field strength. For isometry group of internal space, the SO(n) symmetry and SU(n) symmetry are discussed. And the Kaluza-Klein instanton is also enquired.

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