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Zbl 1166.51013
Tomihisa, Toshio
Geometry of projective plane and Poisson structure. (English)
[J] J. Geom. Phys. 59, No. 5, 673-684 (2009). ISSN 0393-0440

The author proves various identities on Poisson brackets wherefrom he derives the well-known theorems of Desargues, of Pascal, and of Briachon for the real projective plane avoiding any application of the classical Projective Geometry. The author follows the procedure given in [{\it V. Arnold}, J. Geom. Phys. 53, No.~4, 421--427 (2005; Zbl 1092.53055)].
[Rolf Riesinger (Wien)]
MSC 2000:
*51N15 Projective analytic geometry
53D17 Poisson manifolds

Keywords: Poisson bracket; Jacobi identity; Lobachevsky plane; de Sitter world

Citations: Zbl 1092.53055

Cited in: Zbl 1218.53082

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