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

Authors
  • Wang, Pei
Type
Published Article
Publication Date
May 29, 2008
Submission Date
May 29, 2008
Identifiers
DOI: 10.1142/S0217751X09042967
Source
arXiv
License
Yellow
External links

Abstract

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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