A geometrical version of the higher order Hamilton formalism in fibred manifolds
type: Item
instance of: scholarly article
title: A geometrical version of the higher order Hamilton formalism in fibred manifolds
zbMATH Open document ID: 0595.58016
DOI: 10.1016/0393-0440(84)90007-X
published in: Journal of Geometry and Physics
publication date: 1984-01-01T00:00:00Z
review text: The author makes more transparent the fact that an rth order Lagrangian on a fibered manifold \(Y\to X\) does not determine a unique Poincaré- Cartan form provided dim X\(>1\) and \(r>2\) by introducing a new operation generalizing the formal exterior differentiation. He deduces that a unique Poincaré-Cartan form can be determined by means of a simple additional structure - a linear symmetric connection \(\Gamma\) on the base manifold X. Further, by using a suitable geometric definition of a regular \(\gamma\) th order Lagrangian on Y he proves that any Poincaré- Cartan form can be used in the geometrical version of the higher order Hamilton formalism.
reviewed by: B. G. Pachpatte
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 3958279
zbMATH Keywords: Lagrangian on a fibered manifold
zbMATH Keywords: Poincaré-Cartan form
zbMATH Keywords: exterior differentiation
MaRDI profile type: Publication
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full work available at URL: 0393-0440(84)90007-x
OpenAlex ID: W2136059175
author: Ivan Kolář
description: scientific article; zbMATH DE number 3958279