9 citations · 12 across the 6 of their papers we have counts for
6 papers
Covariant derivatives for Ehresmann connections
G. E. Prince, D. J. Saunders
We deal with the construction of covariant derivatives for some quite general Ehresmann connections on fibre bundles. We show how the introduction of a vertical endomorphism allows…
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…
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…
The fundamental form of a homogeneous Lagrangian in two independent variables
D. J. Saunders, M. Crampin
We construct, for a homogeneous Lagrangian of arbitrary order in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian…
The fundamental form of a second-order homogeneous Lagrangian in two variables
D. J. Saunders
We construct, for a second-order homogeneous Lagrangian in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is nul…
Homogeneous variational complexes and bicomplexes
D. J. Saunders
We present a family of complexes playing the same role, for homogeneous variational problems, that the horizontal parts of the variational bicomplex play for variational problems o…