Unified geometry of internal space with space-time

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.