The role of a vector-valued field in multidimensional universe geometry

Details The role of a vector-valued field in multidimensional universe geometry The role of a vector-valued field in multidimensional universe geometry

Nov 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985lmaph..10..315n&link_type=abstract

Letters in Mathematical Physics, Volume 10, Issue 4, pp.315-323

Mathematics

Mathematical Physics

2

Scientific paper

For a model of the multidimensional universe we take a smooth manifold S which under the action of a compact Lie group G fibres into orbits of the same type G/H acquiring the structure of a fibre bundle with typical fibre G/H and base-the orbit space S/G (identified with the four-dimensional spacetime). The notion of a connection form τ on the fibre bundle S→S/G is defined and its role for some geometrical structures on S is considered. In the framework of a theory of G-invariant tensor-type fields on S, it is shown that τ-being itself a field of this type-determines a dimensional reduction of the objects on S to objects on S/G.

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