Geometry of multidimensional universes

Details Geometry of multidimensional universes Geometry of multidimensional universes

Mar 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cmaph..90...79c&link_type=abstract

Communications in Mathematical Physics, Volume 90, Issue 1, pp.79-100

Mathematics

Mathematical Physics

69

Scientific paper

Let G be a compact group of transformation (global symmetry group) of a manifold E (multidimensional universe) with all orbits of the same type (one stratum). We study G invariant metrics on E and show that there is one-to-one correspondence between those metrics and triples ( g μv, A {μ/ä}, h αβ), where g μv is a (pseudo-) Riemannian metric on the space of orbits (space-time), A {μ/ä} is a Yang-Mills field for the gauge group N| H, where N is the normalizer of the isotropy group H in G, and h αβ are certain scalar fields characterizing geometry of the orbits (internal spaces). The scalar curvature of E is expressed in terms of the component fields on M. Examples and model building recipes are also given. The results generalize those of non-abelian Kaluza-Klein theories to the case where internal spaces are not necessarily group manifolds.

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