Form Connections

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1993-05-05

arxiv.org/abs/gr-qc/9305004v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, G\"oteborg, ITP 93-9

Scientific paper

Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein's equations may be written in terms of an SO(3) connection, with SO(3) chosen as an appropriate subgroup of SL(3). We show how a set of "neighbours" of Einstein's equations arises because the subgroup may be chosen in different ways. An explicit example of a non-Einstein metric obtained in this way is given. Some remarks on three dimensional space-times are made.

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