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Canonical forms for separability structures with less than five Killing tensors

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Canonical forms for separability structures with less than five Killing tensors ANNALES DE L’I. H. P., SECTION A SERGIO BENENTI MAURO FRANCAVIGLIA Canonical forms for separability structures with less than five Killing tensors Annales de l’I. H. P., section A, tome 34, no 1 (1981), p. 45-64. <http://www.numdam.org/item?id=AIHPA_1981__34_1_45_0> © Gauthier-Villars, 1981, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A », implique l’accord avec les conditions générales d’utilisation (http://www. numdam.org/legal.php). Toute utilisation commerciale ou impression systé- matique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 45 Canonical forms for separability structures with less than five Killing tensors Sergio BENENTI Mauro FRANCAVIGLIA Istituto di Fisica Matematica and lstituto di Meccanica Razionale, Universita di Torino Ann. Inst. Henri Poincaré, Vol. XXXIV, n° 1, 198L Section A : Physique thdorique. ABSTRACT. review the general theory of separability structures in Riemannian manifolds of arbitrary dimension and signature. Canonical forms for the metric tensor and the Killing tensors associated to separability are computed for structures with at most four Killing tensors. Also the separated ordinary differential equations are listed for each case. This paper covers completely the general framework for dealing with separability structures in General Relativity. 1 INTRODUCTION In previous papers [7, 2, ~ ~] one of us introduced the concept of sepa- rability structure for investigating the integrability by separation of variables of the Hamilton-Jacobi equation for the geodesics of a Riemannian mani- fold (V", g) (1) : This work has been sponsored by Gruppo Nazionale per la Fisica Matematica, Consiglio Nazionale delle Ric

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