The Virasoro group and the fourth geometry of Poincaré

C. Duval; L. Guieu

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arXiv · math/9806135

The Virasoro group and the fourth geometry of Poincaré

C. Duval·L. Guieu

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Abstract

We investigate, in some details, symplectic equivalence between several conformal classes of Lorentz metrics on the hyperboloid of one sheet $H^{1,1} \cong T \times T - Δ$ and affine coadjoint orbits of the group $Diff_+(Δ)$ of orientation preserving diffeomorphisms of $Δ\cong T$ with its natural projective structure. This will allow for generalizations, namely, to the case of arbitrary projective structures on null infinity.

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C. Duval, L. Guieu. 1998-06-24. The Virasoro group and the fourth geometry of Poincaré. https://arxiv.org/abs/math/9806135

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