N-dimensional sl(2)-coalgebra spaces with non-constant curvature

Abstract

An infinite family of ND spaces endowed with sl(2)-coalgebra symmetry is introduced. For all these spaces the geodesic flow is superintegrable, and the explicit form of their common set of integrals is obtained from the underlying sl(2)-coalgebra structure. In particular, ND spherically symmetric spaces with Euclidean signature are shown to be sl(2)-coalgebra spaces. As a byproduct of this construction we present ND generalizations of the classical Darboux surfaces, thus obtaining remarkable superintegrable ND spaces with non-constant curvature.

11 pages. Comments and new references have been added; expressions for scalar curvatures have been corrected and simplified

References in corpus (14)

• Large N Field Theories, String Theory and Gravity
• The General Kerr-de Sitter Metrics in All Dimensions
• Microscopic Formulation of Black Holes in String Theory
• New Einstein-Sasaki Spaces in Five and Higher Dimensions
• Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
• Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes
• Superintegrable Systems in Darboux spaces
• Superintegrability in a two-dimensional space of non-constant curvature
• Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
• Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
• Universal integrals for superintegrable systems on N-dimensional spaces of constant curvature
• Integrability of Particle Motion and Scalar Field Propagation in Kerr-(Anti) de Sitter Black Hole Spacetimes in All Dimensions
• Curvature from quantum deformations
• A Note on Particles and Scalar Fields in Higher Dimensional Nutty Spacetimes

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• (Super)integrability from coalgebra symmetry: formalism and applications
• A new exactly solvable quantum model in N dimensions
• Superintegrable Oscillator and Kepler Systems on Spaces of Nonconstant Curvature via the Stäckel Transform
• On Hamiltonians with position-dependent mass from Kaluza-Klein compactifications
• Quantum Integrals from Coalgebra Structure
• On two superintegrable nonlinear oscillators in N dimensions
• Integrable Henon-Heiles Hamiltonians: a Poisson algebra approach
• Superintegrable anharmonic oscillators on N-dimensional curved spaces
• N-dimensional integrability from two-photon coalgebra symmetry
• Shannon information entropy for a quantum nonlinear oscillator on a space of non-constant curvature
• The classical Darboux III oscillator: factorization, Spectrum Generating Algebra and solution to the equations of motion
• Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system
• New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces
• An infinite family of Dunkl type superintegrable curved Hamiltonians through coalgebra symmetry: Oscillator and Kepler-Coulomb models
• Nonlinear Lie-Hamilton systems: $t$-Dependent curved oscillators and Kepler-Coulomb Hamiltonians
• Exactly solvable deformations of the oscillator and Coulomb systems and their generalization