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Geometry of projective plane and Poisson structure. (English) Zbl 1166.51013
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)].

51N15Projective analytic geometry
53D17Poisson manifolds; Poisson groupoids and algebroids
Full Text: DOI
[1] Arnold, V. I.: Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane, Journal of geometry and physics 53, No. 4, 421-427 (2005) · Zbl 1092.53055 · doi:10.1016/j.geomphys.2004.07.008