Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta
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Publication:1029491
DOI10.1016/j.geomphys.2009.04.010zbMath1169.53054arXiv0803.0289OpenAlexW2091551387WikidataQ115353361 ScholiaQ115353361MaRDI QIDQ1029491
Giuseppe Pucacco, Vladimir S. Matveev, Alexei V. Bolsinov
Publication date: 10 July 2009
Published in: Journal of Geometry and Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0803.0289
Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)
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Cites Work
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- Proof of the projective Lichnerowicz-Obata conjecture
- Compact Liouville surfaces
- Trajectory equivalence and corresponding integrals
- Three-dimensional manifolds having metrics with the same geodesics.
- Hyperbolic manifolds are geodesically rigid
- Quantum integrability of the Beltrami-Laplace operator for geodesically equivalent metrics.
- Geodesic equivalence of metrics on surfaces, and their integrability.
- Geometrical interpretation of Benenti systems
- Projective transformations of pseudo-Riemannian manifolds
- Geodesic equivalence via integrability
- Geodesic mappings of affine-connected and Riemannian spaces
- On complex structures on two-dimensional tori admitting metrics with nontrivial quadratic integral
- 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
- The Maupertuis Principle and Canonical Transformations of the Extended Phase Space
- Quadratic Poisson algebras of two-dimensional classical superintegrable systems and quadratic associative algebras of quantum superintegrable systems
- GEODESIC FLOWS ON TWO-DIMENSIONAL MANIFOLDS WITH AN ADDITIONAL FIRST INTEGRAL THAT IS POLYNOMIAL IN THE VELOCITIES
- Vanishing of the entropy pseudonorm for certain integrable systems
- Geometrical classification of Killing tensors on bidimensional flat manifolds
- Complex variables for separation of the Hamilton-Jacobi equation on real pseudo-Riemannian manifolds
- ( 1 + 1 ) -dimensional separation of variables
- Reciprocal transformations and flat metrics on Hurwitz spaces
- Reciprocal transformations and local Hamiltonian structures of hydrodynamic-type systems
- Stäckel-Equivalent Integrable Hamiltonian Systems
- Killing tensors in two-dimensional space-times with applications to cosmology
- Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry
- Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
- Separation of variables for the Ruijsenaars model and a new integral representation for the Macdonald polynomials
- Metric with ergodic geodesic flow is completely determined by unparameterized geodesics
- An extension of the classical theory of algebraic invariants to pseudo-Riemannian geometry and Hamiltonian mechanics
- Duality between integrable Stäckel systems
- Generalized Stäckel transform and reciprocal transformations for finite-dimensional integrable systems
- Quantum integrability of Beltrami-Laplace operator as geodesic equivalence
