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

Luca Degiovanni | Zendy; Giovanni Rastelli | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

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

Author(s) -

Luca Degiovanni,

Giovanni Rastelli

Publication year - 2007

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.2747611

Subject(s) - hamilton–jacobi equation , separation of variables , mathematics , eigenvalues and eigenvectors , manifold (fluid mechanics) , riemannian manifold , riemannian geometry , formalism (music) , mathematical analysis , pure mathematics , partial differential equation , physics , mechanical engineering , art , musical , quantum mechanics , engineering , visual arts

In this paper the geometric theory of separation of variables fortime-independent Hamilton-Jacobi equation is extended to include the case ofcomplex eigenvalues of a Killing tensor on pseudo-Riemannian manifolds. Thistask is performed without to complexify the manifold but just consideringcomplex-valued functions on it. The simple formalism introduced allows toextend in a very natural way the classical results on separation of variables(including Levi-Civita criterion and Stackel-Eisenhart theory) to the complexcase. Orthogonal variables only are considered.Comment: 26 pages, 5 low resolution picture

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research