Complex variables for separation of the Hamilton-Jacobi equation on real pseudo-Riemannian manifolds

DOI10.1063/1.2747611zbMath1144.81337arXivnlin/0610012OpenAlexW3106449027WikidataQ115333572 ScholiaQ115333572MaRDI QIDQ3529828

Luca Degiovanni, Giovanni Rastelli

Publication date: 14 October 2008

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0610012

Mathematics Subject Classification ID

Hamilton-Jacobi equations in mechanics (70H20) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Canonical transformations in symplectic and contact geometry (53D22) Hamilton-Jacobi theories (49L99)

Related Items (8)

Block-separation of variables: a form of partial separation for natural Hamiltonians ⋮ Nonstandard Separability on the Minkowski Plane ⋮ Invariant classification of the rotationally symmetric R-separable webs for the Laplace equation in Euclidean space ⋮ Killing tensors, warped products and the orthogonal separation of the Hamilton-Jacobi equation ⋮ Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields ⋮ Complete separability of the Hamilton–Jacobi equation for the charged particle orbits in a Liénard–Wiechert field ⋮ Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta ⋮ Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics

Cites Work

• Separable systems of Stäckel
• Variable separation for natural Hamiltonians with scalar and vector potentials on Riemannian manifolds
• Geometrical classification of Killing tensors on bidimensional flat manifolds
• Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
• Remarks on the connection between the additive separation of the Hamilton–Jacobi equation and the multiplicative separation of the Schrödinger equation. I. The completeness and Robertson conditions

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