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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 [V. Arnold, J. Geom. Phys. 53, No. 4, 421–427 (2005; Zbl 1092.53055)].

MSC:

51N15 Projective analytic geometry
53D17 Poisson manifolds; Poisson groupoids and algebroids

Citations:

Zbl 1092.53055
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Full Text: DOI

References:

[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, 4, 421-427 (2005) · Zbl 1092.53055
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