(Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetry
From MaRDI portal
Publication:2331497
DOI10.1016/j.geomphys.2019.07.007zbMath1427.53018arXiv1905.01396OpenAlexW2965142811MaRDI QIDQ2331497
Publication date: 29 October 2019
Published in: Journal of Geometry and Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1905.01396
projectively equivalent metricsprojective connectionsprojective symmetriesintegrable and superintegrable systems
Applications of local differential geometry to the sciences (53B50) Geodesic flows in symplectic geometry and contact geometry (53D25) Projective connections (53B10)
Related Items (5)
3-dimensional Levi-Civita metrics with projective vector fields ⋮ Projectively equivalent 2-dimensional superintegrable systems with projective symmetries ⋮ Metrics admitting projective and c-projective vector fields ⋮ Stäckel equivalence of non-degenerate superintegrable systems, and invariant quadrics ⋮ Normal forms of two-dimensional metrics admitting exactly one essential projective vector field
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Two-dimensional metrics admitting precisely one projective vector field
- Explicit metrics for a class of two-dimensional cubically superintegrable systems
- Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows
- Two-dimensional superintegrable metrics with one linear and one cubic integral
- Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and applications
- Benenti tensors: a useful tool in projective differential geometry
- Geodesically equivalent metrics in general relativity
- Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta
- Riemannian manifolds admitting a projective vector field
- Finding collineations of Kimura metrics
- Geometrical interpretation of Benenti systems
- Geodesic equivalence via integrability
- Bihamiltonian structures and Stäckel separability
- Metrisability of two-dimensional projective structures
- A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields
- Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems
- Completeness of superintegrability in two-dimensional constant-curvature spaces
- Third-order superintegrable systems separable in parabolic coordinates
- Invariant classification of second-order conformally flat superintegrable systems
- An Algebraic Geometric Approach to Separation of Variables
- Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics
- Second order superintegrable systems in conformally flat spaces. III. Three-dimensional classical structure theory
- Projective geometry of systems of second-order differential equations
- Superintegrable systems with third-order integrals of motion
- On the geometry of Grassmannian equivalent connections
- Third-order superintegrable systems separating in polar coordinates
- Superintegrable n=2 systems, quadratic constants of motion, and potentials of Drach
- Bi-differential calculi and bi-Hamiltonian systems
- Metrisability of Painlevé equations
- The Equivalence Problem for Systems of Second-Order Ordinary Differential Equations
- Degree of mobility for metrics of Lorentzian signature and parallel (0,2)-tensor fields on cone manifolds
- Separation of Variables and Superintegrability
- Projectively related metrics, Weyl nullity and metric projectively invariant equations
- Metric connections in projective differential geometry
This page was built for publication: (Super-)integrable systems associated to 2-dimensional projective connections with one projective symmetry