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arXiv · 1611.03447

Lorentzian manifolds with transitive conformal group

Dmitri V. Alekseevsky
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Abstract

We study pseudo-Riemanniasn manifolds $(M,g)$ with transitive group of conformal transformation which is essential, i.e. does not preserves any metric conformal to $g$. All such manifolds of Lorentz signature with non exact isotropy representation of the stability subalgebra are described. A construction of essential conformally homogeneous manifolds with exact isotropy represenatation is given. Using spinor formalism, we prove that it provides all 4-dimensional non conformally flat Lorentzian 4-dimensional manifolds with transitive essentially conformal group.

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Dmitri V. Alekseevsky. 2016-11-10. Lorentzian manifolds with transitive conformal group. https://arxiv.org/abs/1611.03447

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