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] | MR 1340192 | Zbl 0818.53067
- - , Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Springer-Verlag, Berlin, Heidelberg (1995).[3] Geometry of weakly symmetric spaces, J. Math. Soc. Japan, 48 (1996), 745-760. | MR 1404821 | Zbl 0877.53027
- ,[4] 509, Springer-Verlag, Berlin, Heidelberg, New York (1976). | MR 467588 | Zbl 0319.53026
, Contact Manifolds in Riemannian Geometry, Lect. Notes. Math.,[5] | MR 754767 | Zbl 0543.58001
, Groups and Geometric Analysis, Academic Press, Orlando (1984).[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
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