On the three-dimensional spaces which admit a continuous group of motions

General Relativity and Gravitation

Volumn 33, Issue 12, 2001, Pages 2171-2253

  Bianchi, Luigi ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040481441     PISSN: 00017701     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1015357132699     Document Type: Article

References (22)

1. Original title: Sugli spazi a tre dimensioni che ammettono un gruppo continuo di movimenti, Memorie di Matematica e di Fisica della Societa Italiana delle Scienze, Serie Terza, Tomo XI, pp. 267-352 (1898). Printed with the kind permission of the Accademia Nazionale delle Scienze, detta dei XL, in Rome, the current copyright owner. Translated by Robert Jantzen, Department of Mathematical Sciences, Villanova University, Villanova, Pa 19085, USA.
2. This paper was also reprinted in: Opere [The Collected Works of Luigi Bianchi], Rome, Edizione Cremonese, 1952, vol. 9, pp. 17-109.
3. S. Lie-F. Engel, Theorie der Transformationsgruppen, Vol. I (1888), Chap. 18, p. 310 and Vol. III (1893), p. 575. [In the bibliographical footnotes, authors' first initials and, wherever missing, authors' names, have been added by the Editor. Also, journal titles were corrected and details of the citations were added wherever necessary. (Editor)].
4. W. Killing, Über die Grundlagen der Geometrie, Journ. für die reine und angewandte Math. (Crelle), 109 (1892), 121-186.
5. S. Lie-F. Engel, Vol. III, p. 713.
6. See S. Lie-F. Engel, Vol. I, p. 339.
7. S. Lie-F. Engel, Vol. I, p. 502.
8. 2).
9. 3 = 0 which is not integrable.
10. S. Lie-F. Engel, Vol. I, p. 327, and following pages.
11. In Italian: "isomorfismo oleodrico" [Translator].
12. S. Lie-F. Engel, Vol. I, p. 340.
13. 3 on the left in the first commutator; correction after the Opere [Editor].
14. iks and do not lose their validity by limiting them to the consideration of real groups and subgroups, as we do here.
15. S. Lie-F. Engel, Vol. I, p. 204, and following pages.
16. S. Lie-F. Engel, Vol. I, pp. 592-593.
17. See S. Lie-F. Engel, Vol. 1, p. 507, Theor. 104.
18. See the precise discussion in S. Lie-G. Scheffers, pp. 510-511.
19. 3 in the second term; correction after the Opere [Editor].
20. 3 = 0 here, an obvious typo [Editor].
21. S. Lie-F. Engel, Vol 1, §50, p. 186.
22. S. Lie-F. Engel, Vol 1, p. 217.