Abstract
Based on the new point of view on space–time–matter theory developed in our paper (Bejancu, Gen Rel Grav, 2013), we obtain the $$4D$$ Einstein equations in a general $$5D$$ Kaluza–Klein space with electromagnetic potentials. In particular, we recover the $$4D$$ Einstein equations obtained by Wesson and Ponce de Leon (J Math Phys 33:3883, 1992) in case the electromagnetic potentials vanish identically on $$\bar{M}$$ . The Riemannian horizontal connection and the $$4D$$ tensor calculus on $$\bar{M}$$ , are the main tools in the study.
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