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Benenti, Sergio; Francaviglia, Mauro

Canonical forms for separability structures with less than five Killing tensors. (English) Zbl 0454.53030

Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 34, 45-64 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0454.53030

Cited in 2 Documents

MSC:

53C20 Global Riemannian geometry, including pinching
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
83C99 General relativity

Keywords:

Hamilton-Jacobi equation; separability structure; stacked matrix
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References:

[1] S. Benenti , Rend. Sem. Mat. Univ. Pol. Torino , t. 34 , 1975 - 1976 , p. 431 - 463 . MR 474131 | Zbl 0346.53008 · Zbl 0346.53008
[2] S. Benenti , C. R. A. S. , Paris , t. 283 A, 1976 , p. 215 - 218 ; Rep. Math. Phys. , t. 12 , 1977 , p. 311 - 316 . MR 433506 | Zbl 0349.53014 · Zbl 0349.53014
[3] S. Benenti , C. R. A. S. , Paris , t. 289 A, 1979 , p. 795 - 798 . MR 558800 | Zbl 0431.53020 · Zbl 0431.53020
[4] S. Benenti , Separability structures in Riemannian manifolds , in: Proceed. Conf. Diff. Geom. Methods in Math. Phys., Salamanca , 1979 , P. Garcia and A. Perez-Randon Eds. ( Lect. Notes in Math ; Springer , forthcoming). · Zbl 0459.53019
[5] S. Benenti , M. Francaviglia , Ann. Inst. H. Poincaré , t. 30 , 1979 , p. 143 - 157 . Numdam | MR 535370 | Zbl 0459.53019 · Zbl 0459.53019
[6] R. Kalnins , J.W. Miller , Killing tensors and nonorthogonal variable separation for Hamilton-Jacobi equations , preprint, 1980 . · Zbl 0454.70023 · doi:10.1137/0511089
[7] T. Levi-Civita , Math. Ann. , t. 59 , 1904 , p. 383 - 397 . MR 1511275 | JFM 35.0362.02 · JFM 35.0362.02
[8] S. Benenti , M. Francaviglia , GRG Journal , t. 10 , 1979 , p. 79 - 92 . Zbl 0438.53023 · Zbl 0438.53023 · doi:10.1007/BF00757025
[9] B. Carter , Comm. Math. Phys. , t. 10 , 1968 , p. 280 - 310 . Article | MR 239841 | Zbl 0162.59302 · Zbl 0162.59302
[10] C. Boyer , R. Kalnins , J.W. Miller , Comm. Math. Phys. , t. 59 , 1978 , p. 285 - 302 . Article | MR 488109 | Zbl 0377.53009 · Zbl 0377.53009 · doi:10.1007/BF01611508
[11] S. Benenti , M. Francaviglia , The theory of separability of the Hamilton-Jacobi equation and its applications to General Relativity , Ch. 13, in: General Relativity and Gravitation , vol. I , A. Held Ed. ( Plenum Press , New York , 1980 ). MR 583725
[12] M. Francaviglia , Separability of Einstein space-times: the state of the art , in: Procceeding 2nd Marcell Grossmann Meeting , Trieste 1979 , R. Ruffini Ed. (forthcoming). MR 678953
[13] M. Francaviglia , On the canonical forms of all separable metrics (in preparation).
[14] C. Boyer , Separation of variables in Einstein spaces II. No ignorable coordinates , preprint n. 217, Inst. de Invest. en Mat. Aplicadas y en Sistemas, Univ. of Mexico City , 1979 ; forthcoming in GRG Journal . MR 601482 | Zbl 0467.53018 · Zbl 0467.53018 · doi:10.1007/BF00771864
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