Proviamo che tutti gli spazi semplicemente connessi -simmetrici sono debolmente simmetrici e quindi commutativi.
@article{BUMI_1999_8_2B_2_389_0,
author = {J\"urgen Berndt and Lieven Vanhecke},
title = {$\phi$-symmetric spaces and weak symmetry},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {2-A},
year = {1999},
pages = {389-392},
zbl = {0978.53091},
mrnumber = {1706568},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_1999_8_2B_2_389_0}
}
Berndt, Jürgen; Vanhecke, Lieven. $\phi$-symmetric spaces and weak symmetry. Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999) pp. 389-392. http://gdmltest.u-ga.fr/item/BUMI_1999_8_2B_2_389_0/
[1] , , , Examples of weakly symmetric spaces in contact geometry, Boll. Un. Mat. Ital., (7) 11-B (1997), Suppl. fasc. 2, 1-10. | MR 1456247 | Zbl 0880.53041
[2] --, Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Springer-Verlag, Berlin, Heidelberg (1995). | MR 1340192 | Zbl 0818.53067
[3] -, Geometry of weakly symmetric spaces, J. Math. Soc. Japan, 48 (1996), 745-760. | MR 1404821 | Zbl 0877.53027
[4] , Contact Manifolds in Riemannian Geometry, Lect. Notes. Math., 509, Springer-Verlag, Berlin, Heidelberg, New York (1976). | MR 467588 | Zbl 0319.53026
[5] , Groups and Geometric Analysis, Academic Press, Orlando (1984). | MR 754767 | Zbl 0543.58001
[6] , Stiefel manifolds and non-commutative -symmetric spaces, preprint.
[7] -, The classification of -symmetric Sasakian manifolds, Monatsh. Math., 115 (1993), 83-98. | MR 1223246 | Zbl 0781.53038
[8] --, D'Atri spaces, in Topics in Geometry, In Memory of Joseph D'Atri, Birkhäuser, Boston, Basel, Berlin (1996), 241-284. | MR 1390318 | Zbl 0862.53039
[9] , Commutative spaces which are not weakly symmetric, Bull. London Math. Soc., to appear. | MR 1479033 | Zbl 0921.22007
[10] , Modified -type groups and symmetric-like Riemannian spaces, preprint 1997. | MR 1669469 | Zbl 0942.53034
[11] , Reflective submanifolds. III. Congruency of isometric reflective submanifolds and corrigenda to the classification of reflective submanifolds, J. Diff. Geom., 14 (1979), 167-177. | MR 587545 | Zbl 0453.53044
[12] , Horizontal lifts of isometric immersions into the bundle space of a pseudo-Riemannian submersion, in Global Differential Geometry and Global Analysis 1984, Lect. Notes Math., 1156, Springer-Verlag, Berlin, Heidelberg, New York (1985), 264-279. | MR 824074 | Zbl 0566.53025
[13] , Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc., 20 (1956), 47-87. | MR 88511 | Zbl 0072.08201
[14] , Sasakian -symmetric spaces, Tôhoku Math. J., 29 (1977), 91-113. | MR 440472 | Zbl 0343.53030
[15] , Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tôhoku Math. J., 36 (1984), 293-314. | MR 742600 | Zbl 0528.53047