Unified geometry of internal space with space-time

Abstract

The unified theory of gravitation with gauge fields proposed earlier is shown to be a ($4+n$)-dimensional Einstein theory with $n$ linearly independent complete spacelike Killing vector fields which span an $n$-dimensional metric submanifold and form a closed Lie algebra. In this picture the internal space is combined with space-time and the internal symmetry becomes a symmetry of the metric of the ($4+n$)-dimensional combined space. The 4-dimensional space-time appears as the quotient space of the ($4+n$)-dimensional enlarged space by the equivalence relation of the group of motions of the $n$ Killing vector fields.