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Berndt, Jürgen and Vanhecke, Lieven:
$\phi$-symmetric spaces and weak symmetry
Bollettino dell'Unione Matematica Italiana Serie 8 2-B (1999), fasc. n.2, p. 389-392, Unione Matematica Italiana (English)
pdf (206 Kb), djvu (71 Kb). | MR1706568 | Zbl 0978.53091

Sunto

Proviamo che tutti gli spazi semplicemente connessi $\phi$-simmetrici sono debolmente simmetrici e quindi commutativi.
Referenze Bibliografiche
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[2] J. BERNDT - F. TRICERRI - L. VANHECKE , Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Springer-Verlag, Berlin, Heidelberg (1995). | MR 1340192 | Zbl 0818.53067
[3] J. BERNDT - L. VANHECKE , Geometry of weakly symmetric spaces, J. Math. Soc. Japan, 48 (1996), 745-760. | fulltext mini-dml | MR 1404821 | Zbl 0877.53027
[4] D. E. BLAIR , Contact Manifolds in Riemannian Geometry, Lect. Notes. Math., 509, Springer-Verlag, Berlin, Heidelberg, New York (1976). | MR 467588 | Zbl 0319.53026
[5] S. HELGASON , Groups and Geometric Analysis, Academic Press, Orlando (1984). | MR 754767 | Zbl 0543.58001
[6] J. A. JIMÉNEZ , Stiefel manifolds and non-commutative $\phi$-symmetric spaces, preprint.
[7] J. A. JIMÉNEZ - O. KOWALSKI , The classification of $\phi$-symmetric Sasakian manifolds, Monatsh. Math., 115 (1993), 83-98. | MR 1223246 | Zbl 0781.53038
[8] O. KOWALSKI - F. PRÜFER - L. VANHECKE , 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] J. LAURET , Commutative spaces which are not weakly symmetric, Bull. London Math. Soc., to appear. | MR 1479033 | Zbl 0921.22007
[10] J. LAURET , Modified $H$-type groups and symmetric-like Riemannian spaces, preprint 1997. | MR 1669469 | Zbl 0942.53034
[11] D. S. P. LEUNG , Reflective submanifolds. III. Congruency of isometric reflective submanifolds and corrigenda to the classification of reflective submanifolds, J. Diff. Geom., 14 (1979), 167-177. | fulltext mini-dml | MR 587545 | Zbl 0453.53044
[12] H. RECKZIEGEL , 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] A. SELBERG , 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] T. TAKAHASHI , Sasakian $\phi$-symmetric spaces, Tôhoku Math. J., 29 (1977), 91-113. | fulltext mini-dml | MR 440472 | Zbl 0343.53030
[15] M. TAKEUCHI , Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tôhoku Math. J., 36 (1984), 293-314. | fulltext mini-dml | MR 742600 | Zbl 0528.53047

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