×

Conformally flat pseudo-symmetric spaces of constant type. (English) Zbl 1164.53339

Summary: We give the complete classification of conformally flat pseudo-symmetric spaces of constant type.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C35 Differential geometry of symmetric spaces
PDF BibTeX XML Cite
Full Text: DOI EuDML Link

References:

[1] E. Boeckx, O. Kowalski and L. Vanhecke: Riemannian Manifolds of Conullity Two. World Scientific, 1996. · Zbl 0904.53006
[2] G. Calvaruso: Conformally flat semi-symmetric spaces. Arch. Math. Brno 41 (2005), 27–36. · Zbl 1114.53027
[3] G. Calvaruso and L. Vanhecke: Special ball-homogeneous spaces. Z. Anal. Anwendungen 16 (1997), 789–800. · Zbl 0892.53023
[4] R. Deszcz: On pseudo-symmetric spaces. Bull. Soc. Math. Belgium, Série A 44 (1992), 1–34. · Zbl 0808.53012
[5] N. Hashimoto and M. Sekizawa: Three-dimensional conformally flat pseudo-symmetric spaces of constant type. Arch. Math. (Brno) 36 (2000), 279–286. · Zbl 1054.53060
[6] O. Kowalski and M. Sekizawa: Pseudo-symmetric spaces of constant type in dimension three. Rendiconti di Matematica, Serie VII 17 (1997), 477–512. · Zbl 0889.53026
[7] R. S. Kulkarni: Curvature structures and conformal transformations. J. Differential Geom. 4 (1970), 425–451. · Zbl 0206.24403
[8] P. Ryan: A note on conformally flat spaces with constant scalar curvature. Proc. 13th Biennal Seminar of the Canadian Math.Congress Differ. Geom. Appl., Dalhousie Univ. Halifax 1971 2 (1972), 115–124. · Zbl 0267.53024
[9] Z. I. Szabó: Structure theorems on Riemannian manifolds satisfying R(X, Y) {\(\cdot\)} R = 0, I, the local version. J. Diff. Geom. 17 (1982), 531–582. · Zbl 0508.53025
[10] H. Takagi: An example of Riemannian manifold satisfying R(X, Y) {\(\cdot\)} R but not = 0. Tôhoku Math. J. 24 (1972), 105–108. · Zbl 0237.53041
[11] H. Takagi: Conformally flat Riemannian manifolds admitting a transitive group of isometries. Tohôku Math. J. 27 (1975), 103–110. · Zbl 0311.53062
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.