8 research outputs found
symmetries of the Ricci tensor of static space times with maximal symmetric transverse spaces
Static space times with maximal symmetric transverse spaces are classified
according to their Ricci collineations. These are investigated for
non-degenerate Ricci tensor (). It turns out that the
only collineations admitted by these spaces can be ten, seven, six or four.
Some new metrics admitting proper Ricci collineations are also investigated.Comment: 11 page
Lie and Noether symmetries of geodesic equations and collineations
The Lie symmetries of the geodesic equations in a Riemannian space are
computed in terms of the special projective group and its degenerates (affine
vectors, homothetic vector and Killing vectors) of the metric. The Noether
symmetries of the same equations are given in terms of the homothetic and the
Killing vectors of the metric. It is shown that the geodesic equations in a
Riemannian space admit three linear first integrals and two quadratic first
integrals. We apply the results in the case of Einstein spaces, the
Schwarzschild spacetime and the Friedman Robertson Walker spacetime. In each
case the Lie and the Noether symmetries are computed explicitly together with
the corresponding linear and quadratic first integrals.Comment: 19 page
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
Topological defect solutions in the spherically symmetric space-time admitting conformal motion
This paper has excessive overlap with the following papers also written by
the authors or their collaborators: hep-th/0505013 and 0705.2930.Comment: This submission has been withdrawn by arXiv administrators due to
inappropriate text reuse from external source