11 citations · 24 across the 9 of their papers we have counts for
9 papers
Quadratic forms and the expansion and rotations of linear endomorphisms
Geoff Prince
New expansionary and rotational quadratic forms are constructed for -endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are establ…
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…
The inverse problem in the calculus of variations: new developments
Thoan Do, Geoff Prince
We deal with the problem of determining the existence and uniqueness of Lagrangians for systems of second order ordinary differential equations. A number of recent theorems are…
Torsion and the second fundamental form for distributions
G. E. Prince
The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally…
An intrinsic and exterior form of the Bianchi identities
Thoan Do, Geoff Prince
We give an elegant formulation of the structure equations (of Cartan) and the Bianchi identities in terms of exterior calculus without reference to a particular basis and without t…
New progress in the inverse problem in the calculus of variations
Thoan Do, Geoff Prince
We present a new class of solutions for the inverse problem in the calculus of variations in arbitrary dimension . This is the problem of determining the existence and uniquenes…
Evolution equations: Frobenius integrability, conservation laws and travelling waves
Geoff Prince, Naghmana Tehseen
We give new results concerning the Frobenius integrability and solution of evolution equations admitting travelling wave solutions. In particular, we give a powerful result which e…
Integration of PDEs by differential geometric means
Naghmana Tehseen, Geoff Prince
We use Vessiot theory and exterior calculus to solve partial differential equations(PDEs) of the type uyy = F(x, y,u,ux,uy,uxx,uxy) and associated evolution equations. These equati…
Time-dependent kinetic energy metrics for Lagrangians of electromagnetic type
W. Sarlet, G. Prince, T. Mestdag +1
We extend the results obtained in a previous paper about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explic…