Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces
By Gloria Marí Beffa. 2005
50 citations recorded by the source corpus.
In this paper we describe a family of compatible Poisson structures defined on the space of coframes (or differential invariants) of curves in flat homogeneous spaces of the form M ≅ (G x R n )/G where G C GL(n,R) is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold M so that the induced evolution on their differential invariants is Hamiltonian with respect to our main Hamiltonian bracket.
Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3f799c520dae49c92950fedf675410d7b42a2ce5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
In Statistical and Nonlinear Physics
- Peter J. Olver
- Juha Pohjanpelto
- Gloria Marí Beffa
- G. Misiołek
- A. Alexandrou Himonas
- Yue Liu
- Changzheng Qu
- Yong Zhou
Citations in the corpus
- Generating differential invariants (2007, methodology): “Further applications can be found, for instance, in the work of Maŕı Beffa, [14, 15, 16], on the Poisson geometry of curves and surfaces in homogeneous spaces, and Mansfield, [13], on symmetric differential equations.”