The projective Cartan-Klein geometry of the Helmholtz conditions

DOI10.3934/jgm.2018003zbMath1412.49087OpenAlexW2776437447MaRDI QIDQ1711938

Carlos Eduardo Durán, Diego Otero

Publication date: 18 January 2019

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/jgm.2018003

zbMATH Keywords

Schwarziandifferential invariantsHelmholtz conditionsLagrangian Grassmannian manifoldprojective differential equationsSarlet-Engels-Bahar conditions

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Variational problems in a geometric measure-theoretic setting (49Q20) Linear ordinary differential equations and systems (34A30)

Cites Work

• Geometry of fanning curves in divisible Grassmannians
• Geometric invariants of fanning curves
• Time-dependent linear systems derivable from a variational principle
• Moving planes, Jacobi curves and the dynamical approach to Finsler geometry
• The projective symplectic geometry of higher order variational problems: minimality conditions
• The Schwarzian as a curvature
• The inverse problem of Lagrangian dynamics for higher-order differential equations: a geometrical approach
• Curvature: A Variational Approach
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