4D Einstein equations in a general gauge Kaluza–Klein space

Using the new approach on higher-dimensional Kaluza–Klein theories developed by the first author, we obtain the 4D Einstein equations on a (4 + n)D relativistic gauge Kaluza–Klein space. Adapted frame and coframe fields, adapted tensor fields, and the Riemannian adapted connection, have a fundamental role in the study. The high level of generality of the study, enables us to recover several results from earlier papers on this matter.