Quantum integrability for the Beltrami-Laplace operators of projectively equivalent metrics of arbitrary signatures

Abstract

We generalize the result of [Matveev-Topalov 2001] to all signatures: we show that in all signatures the Killing tensors constructed by projectively equivalent metrics correspond to commuting differential operators

References in corpus (4)

• Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems
• The geodesic flow of a generic metric does not admit nontrivial integrals polynomial in momenta
• Projectively related metrics, Weyl nullity, and metric projectively invariant equations
• Modified Laplace-Beltrami quantization of natural Hamiltonian systems with quadratic constants of motion