Linear connection in theories of Kaluza-Klein type (Q797156)

The physical ideas by Kaluza-Klein are mathematically correct only when the manifold M is equipped with a projection \(\pi:M\to M_ 4\) and all physical \((=geometrical)\) constructions are consistent with this \(\pi\) [the reviewer, Tr. Semin. Vetorn. Tenzorn. Anal. Prilozh. Geom. Mekh. Fiz. 14, 154-173 (1968; Zbl 0169.239)]. The author takes \(M=M_{4+n}\) and introduces a linear connection with such a property. Some remarks on Lagrange functions are suggested. No theorems are given.