Linear connection in theories of Kaluza–Klein type

A linear connection on a principal fiber bundle is proposed for which the scalar curvature is a sum of Lagrangians of gauge fields and of the general theory of relativity. The linear connection is constructed on the basis of requirements that have a geometrical meaning. and it possesses torsion. The presence or absence of a cosmological constant depends on the choice of the linear connection on the structure group, which can be an arbitrary Lie group.