Separability in Riemannian Manifolds

Abstract

An outline of the basic Riemannian structures underlying the separation of variables in the Hamilton-Jacobi equation of natural Hamiltonian systems.

This paper was submitted in 2004 to the Royal Society and accepted for publication in a special volume dedicated to the 'State of the Art of the Separation of Variables'. However, this volume was never published due to death of the Editor, V. Kutznetsov

References in corpus (6)

• Quasi-Lagrangian Systems of Newton Equations
• Separation of variables in quasi-potential systems of bi-cofactor form
• Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems
• Construction of coupled Harry Dym hierarchy and its solutions from Stäckel systems
• From Stäckel systems to integrable hierarchies of PDE's: Benenti class of separation relations
• Stackel separability for Newton systems of cofactor type

Cited by in corpus (20)

• Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.0)
• Shapovalov wave-like spacetimes
• Algebra of the symmetry operators of the Klein-Gordon-Fock equation for the case when groups of motions $G_3$ act transitively on null subsurfaces of spacetime
• Algebras of integrals of motion for the Hamilton-Jacobi and Klein-Gordon-Fock equations in spacetime with a four-parameter groups of motions in the presence of an external electromagnetic field
• Separation of variables in Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle in the Stackel spaces of type (1.1)
• Covariants,joint invariants and the problem of equivalence in the invariant theory of Killing tensors defined in pseudo-Riemannian spaces of constant curvature
• Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature
• Constructing a complete integral of the Hamilton-Jacobi equation on pseudo-Riemannian spaces with simply transitive groups of motions
• Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
• On integrable systems outside Nijenhuis and Haantjes geometry
• Killing tensors, Warped Products and The Orthogonal Separation of The Hamilton-Jacobi Equation
• Normal forms of two-dimensional metrics admitting exactly one essential projective vector field
• On projective and affine equivalence of sub-Riemannian metrics
• Concircular tensors in Spaces of Constant Curvature: With Applications to Orthogonal Separation of The Hamilton-Jacobi Equation
• Separability and Symmetry Operators for Painlevé Metrics and their Conformal Deformations
• Inverse scattering at fixed energy on three-dimensional asymptotically hyperbolic St{ä}ckel manifolds
• Second order Killing tensors related to symmetric spaces
• Trihamiltonian extensions of separable systems in the plane
• Separability in Consistent Truncations
• Non-existence of orthogonal coordinates on the complex and quaternionic projective spaces