28 research outputs found
Projective dynamics and first integrals
We present the theory of tensors with Young tableau symmetry as an efficient
computational tool in dealing with the polynomial first integrals of a natural
system in classical mechanics. We relate a special kind of such first
integrals, already studied by Lundmark, to Beltrami's theorem about
projectively flat Riemannian manifolds. We set the ground for a new and simple
theory of the integrable systems having only quadratic first integrals. This
theory begins with two centered quadrics related by central projection, each
quadric being a model of a space of constant curvature. Finally, we present an
extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure
Algebraic theory of affine curvature tensors
We use curvature decompositions to construct generating sets for the space of
algebraic curvature tensors and for the space of tensors with the same
symmetries as those of a torsion free, Ricci symmetric connection; the latter
naturally appear in relative hypersurface theory.Comment: The paper is dedicated to the memory of the first author (N. Blazic)
who passed away Monday 10 October 200
The structure of algebraic covariant derivative curvature tensors
We use the Nash embedding theorem to construct generators for the space of
algebraic covariant derivative curvature tensors