On $n$-dimensional Riemannian spaces admitting a group of motions of order $n(n-1)/2+1$
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- Trans. Amer. Math. Soc. 74 (1953), 260-279 Request permission
References
-
L. Bianchi, Lezioni di geometria differenziale, 3d ed., vol. II.
- É. Cartan, Leçons sur la Géométrie des Espaces de Riemann, Gauthier-Villars, Paris, 1946 (French). 2d ed. MR 0020842
- I. P. Egorov, On a strengthening of Fubini’s theorem on the order of the group of motions of a Riemannian space, Doklady Akad. Nauk SSSR (N.S.) 66 (1949), 793–796 (Russian). MR 0031809 L. P. Eisenhart, Continuous groups of transformations, Princeton University Press, 1933. G. Fubini, Sugli spazii che ammettono un gruppo continuo di movimenti, Annali di Matematica (3) vol. 8 (1903) pp. 39-81.
- Deane Montgomery and Hans Samelson, Transformation groups of spheres, Ann. of Math. (2) 44 (1943), 454–470. MR 8817, DOI 10.2307/1968975 P. Rachevsky, Caractères tensoriels de l’espace sous-projectif, Abhandlungen des Seminars für Vektor- und Tensoranalysis. Moskou vol. 1 (1933) pp. 126-140.
- Hsien-Chung Wang, On Finsler spaces with completely integrable equations of Killing, J. London Math. Soc. 22 (1947), 5–9. MR 22431, DOI 10.1112/jlms/s1-22.1.5
- Kentaro Yano, Concircular geometry. II. Integrability conditions of $\rho _{\mu \nu }=\phi g_{\mu \nu }$, Proc. Imp. Acad. Tokyo 16 (1940), 354–360. MR 3114
- Kentaro Yano, Sur le parallélisme et la concourance dans l’espace de Riemann, Proc. Imp. Acad. Tokyo 19 (1943), 189–197 (French). MR 14287 —, Groups of transformations in generalized spaces, Tokyo, 1949.
- Kentaro Yano and Tyuzi Adati, On certain spaces admitting concircular transformations, Proc. Japan Acad. 25 (1949), 188–195. MR 52861
Additional Information
- © Copyright 1953 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 74 (1953), 260-279
- MSC: Primary 53.0X
- DOI: https://doi.org/10.1090/S0002-9947-1953-0052860-X
- MathSciNet review: 0052860