Abstract
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 ⋉ R n ) / G \mathcal {M} \cong (G\ltimes \mathbb {R}^n)/G where G ⊂ G L ( n , R ) G\subset {\mathrm {GL}}(n,\mathbb {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 \mathcal {M} so that the induced evolution on their differential invariants is Hamiltonian with respect to our main Hamiltonian bracket.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.