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8 papers · 1 filter
Curvature of quaternionic skew-Hermitian manifolds and bundle constructions
Ioannis Chrysikos, Vicente Cortés, Jan Gregorovič
This articles is devoted to a description of the second-order differential geometry of torsion-free almost quaternionic skew-Hermitian manifolds, that is, of quaternionic skew-Herm…
On Lagrangians with Reduced-Order Euler-Lagrange Equations
David Saunders
If a Lagrangian defining a variational problem has order then its Euler-Lagrange equations generically have order . This paper considers the case where the Euler-Lagrange e…
Shape maps for second order partial differential equations
O. Rossi, D. J. Saunders, G. E. Prince
We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a cong…
Implicit Lagrange-Routh Equations and Dirac Reduction
Eduardo García-Toraño Andrés, Tom Mestdag, Hiroaki Yoshimura
In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian…
Tangent bundle geometry induced by second order partial differential equations
D. J. Saunders, O. Rossi, G. E. Prince
We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection…
Hilbert forms for a Finsler metrizable projective class of sprays
M. Crampin, T. Mestdag, D. J. Saunders
The projective Finsler metrizability problem deals with the question whether a projective-equivalence class of sprays is the geodesic class of a (locally or globally defined) Finsl…