Rocky Mountain Journal of Mathematics

A New Class of Weakly Symmetric Spaces

J.C. González-Dávila and L. Vanhecke

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 29, Number 3 (1999), 853-872.

First available in Project Euclid: 5 June 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]

Weakly symmetric spaces Killing-transversally symmetric spaces


González-Dávila, J.C.; Vanhecke, L. A New Class of Weakly Symmetric Spaces. Rocky Mountain J. Math. 29 (1999), no. 3, 853--872. doi:10.1216/rmjm/1181071613.

Export citation


  • J. Berndt, O. Kowalski and L. Vanhecke, Geodesics in weakly symmetric spaces, Ann. Global Anal. Geom. 15 (1997), 153-156.
  • J. Berndt, F. Prüfer and L. Vanhecke, Symmetric-like Riemannian manifolds and geodesic symmetries, Proc. Roy. Soc. Edinburgh 125 (1995), 265-282.
  • J. Berndt, F. Ricci and L. Vanhecke, Weakly symmetric groups of Heisenberg type, Differential Geom. Appl. 8 (1998), 275-284.
  • J. Berndt, Ph. Tondeur and L. Vanhecke, Examples of weakly symmetric spaces in contact geometry, Boll. Un. Mat. Ital. 11-B (1997), suppl. fasc. 2, 1-10.
  • J. Berndt, F. Tricerri and L. Vanhecke, Generalized Heisenberg groups and Damek-Ricci harmonic spaces, Lecture Notes in Math. 1598 (1995).
  • J. Berndt and L. Vanhecke, Geometry of weakly symmetric spaces, J. Math. Soc. Japan 48 (1996), 745-760.
  • --------, $\vp$-symmetric spaces and weak symmetry, Boll. Un. Mat. Ital., to appear.
  • A.L. Besse, Einstein manifolds, Ergeb. Math. Grenzgeb. (3) 10 (1987).
  • D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math. 509 (1976).
  • B.Y. Chen and L. Vanhecke, Isometric, holomorphic and symplectic reflections, Geom. Dedicata 29 (1989), 259-277.
  • J.C. González-Dávila, M.C. González-Dávila and L. Vanhecke, Reflections and isometric flows, Kyungpook Math. J. 35 (1995), 113-144.
  • --------, Classification of Killing-transversally symmetric spaces, Tsukuba J. Math. 20 (1996), 321-347.
  • --------, Invariant submanifolds in flow geometry, J. Austral. Math. Soc. 62 (1997), 290-314.
  • J.C. González-Dávila and L. Vanhecke, New examples of weakly symmetric spaces, Monatsh. Math. 125 (1998), 309-314.
  • O. Kowalski and R.A. Marinosci, Weakly symmetric spaces in dimension five, J. Geom. 58 (1997), 123-131.
  • D.S.P. Leung, Reflective submanifolds, III. Congruency of isometric reflective submanifolds and corrigenda to the classification of reflective submanifolds, J. Differential Geom. 14 (1979), 167-177.
  • S. Nagai, Weakly symmetric spaces in complex and quaternionic space forms, Arch. Math. 65 (1995), 342-351.
  • K. Ogiue, On fiberings of almost contact manifolds, Kōdai Math. Sem. Rep. 17 (1965), 53-62.
  • B. O'Neill, The fundamental equation of a submersion, Michigan Math. J. 13 (1966), 459-469.
  • H. Reckziegel, Horizontal lifts of isometric immersions into the bundle space of a pseudo-Riemannian submersion, in Global differential geometry and global analysis (D. Ferus, R.B. Gardner, S. Helgason and U. Simon, eds.), Lecture Notes in Math. 1156 (1976), 264-279.
  • --------, A correspondence between horizontal submanifolds of Sasakian manifolds and totally real submanifolds of Kählerian manifolds, in Topics in differential geometry, I, II (J. Szenthe and L. Tamássy, eds.), North-Holland, Amsterdam, 1988, 1063-1081.
  • B.L. Reinhart, Differential geometry of foliations, Ergeb. Math. Grenzgeb. (3) 99 (1983).
  • 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.
  • T. Takahashi, Sasakian $\vp$-symmetric spaces, Tôhoku Math. J. 29 (1977), 91-113.
  • M. Takeuchi, Stability of certain minimal submanifolds of compact Hermitian symmetric spaces, Tôhoku Math. J. 36 (1984), 293-314.
  • Ph. Tondeur, Foliations on Riemannian manifolds, Universitext, Springer-Verlag, Berlin, 1988.
  • Ph. Tondeur and L. Vanhecke, Transversally symmetric Riemannian foliations, Tôhoku Math. J. 42 (1990), 307-317.
  • K. Yano and M. Kon, Structures on manifolds, World Scientific, Singapore, 1984.
  • W. Ziller, Weakly symmetric spaces, in Topics in Geometry: In memory of Joseph D'Atri, (S. Gindikin, ed.), Progr. Nonlinear Differential Equations Appl. 20 Birkhäuser, Boston, 1996, 355-368.