Geometry of projective plane and Poisson structure
type: Item
instance of: scholarly article
title: Geometry of projective plane and Poisson structure
zbMATH Open document ID: 1166.51013
author: Toshio Tomihisa
published in: Journal of Geometry and Physics
publication date: 2009-05-19T00:00:00Z
review text: 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 [\textit{V. Arnold}, J. Geom. Phys. 53, No.~4, 421--427 (2005; Zbl 1092.53055)].
reviewed by: Rolf Riesinger
Mathematics Subject Classification ID: 51N15
Mathematics Subject Classification ID: 53D17
zbMATH DE Number: 5554728
zbMATH Keywords: Poisson bracket
zbMATH Keywords: Jacobi identity
zbMATH Keywords: Lobachevsky plane
zbMATH Keywords: de Sitter world
MaRDI profile type: Publication
full work available at URL: j.geomphys.2009.02.005
OpenAlex ID: W2014212704
cites work: Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane
DOI: 10.1016/J.GEOMPHYS.2009.02.005
description: scientific article; zbMATH DE number 5554728