Universal Features of Dimensional Reduction Schemes from General Covariance Breaking

Understand

Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates.

• By investigating residual covariance we introduce lower dimensional tensors --generalizing to one side Kaluza-Klein gauge fields and to the other side extrinsic curvature and torsion of embedded spaces-- fully characterizing the geometry of dimensional reduction.
• We obtain general formulas for the reduction of the main tensors and operators of Riemannian geometry.
• In particular, we provide what is probably the maximal possible generalization of Gauss, Codazzi and Ricci equations and various other standard formulas in Kaluza-Klein and embedded spacetimes theories.