On the alternative description of complex holomorphic and Lorentz geometries in four dimensions

Details On the alternative description of complex holomorphic and Lorentz geometries in four dimensions On the alternative description of complex holomorphic and Lorentz geometries in four dimensions

1993-12-29

arxiv.org/abs/gr-qc/9312038v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages, uuencoded compressed PostScript, no local #

Scientific paper

The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is spread to the metric case in terms of notion of normalized ordered oriented transection field. As a result, one obtains a possibility to handle the metric geometry without any references to the metric tensor itself on a distinct base which nevertheless contains all the information on metricity. Moreover, the notion of space-time curvature is provided with its natural counterpart in the transection `language' in a form of curvature endomorphism as well. To globalize the local constructions introduced, a certain fiber bundle is defined whose sections are equivalent to normalized ordered oriented transection fields and locally to the metric tensor on space-time. The criterion distinguishing the Lorentz geometry is discussed. The resulting alternative method of the description of space-time metricity, dealing with exterior forms foliation alone, seems to be of a power compatible with one of the standard concept based on the metric tensor.

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