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Zbl 1092.53055
Arnold, V.
Lobachevsky triangle altitudes theorem as the Jacobi identity in the Lie algebra of quadratic forms on symplectic plane. (English)
[J] J. Geom. Phys. 53, No. 4, 421-427 (2005). ISSN 0393-0440

Author's abstract: An isomorphism between the Lobachevsky and de Sitter's world geometries with the symplectic geometry and the Lie algebra of binary quadratic forms is used to derive the altitudes concurrence for the Lobachevsky and de Sitter triangles.
[Iskander A. Taimanov (Novosibirsk)]
MSC 2000:
*53D05 Symplectic manifolds, general

Keywords: projective geometry; de Sitter world; symplectic algebra; Klein model

Cited in: Zbl 1218.53082 Zbl 1204.53064 Zbl 1166.51013

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Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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