Killing Tensors and Nonorthogonal Variable Separation for Hamilton–Jacobi Equations | Zendy

E. G. Kalnins | Zendy; Willard Miller | Zendy

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Killing Tensors and Nonorthogonal Variable Separation for Hamilton–Jacobi Equations

Author(s) -

E. G. Kalnins,

Willard Miller

Publication year - 1981

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/0512054

Subject(s) - hamilton–jacobi equation , mathematics , converse , separable space , riemannian manifold , pure mathematics , separation of variables , manifold (fluid mechanics) , mathematical analysis , variable (mathematics) , involution (esoterism) , partial differential equation , geometry , mechanical engineering , politics , political science , law , engineering

Every separable coordinate system for the Hamilton–Jacobi equation on a Riemannian manifold $V_n $ corresponds to a family of $n - 1$ Killing tensors in involution, but the converse is false. For general n we find a practical characterization of those involutive families of Killing tensors that correspond to variable separation, orthogonal or not.

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