ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53 Koda, Takashi, Toyama University, Japan Weakly symmetric property of Riemannian 3-symmetric spaces. The notion of weakly symmetric spaces has been introduced by A. Selberg. Recently, their geometric characterizations are given by J. Berndt and L. Vanhecke, and a useful one by W. Ziller. We first show that if a nearly Kähler manifold is weakly symmetric and its pseudo-holomorphic isometry group acts transitively on it, then it is a Riemannian 3-symmetric space. And then it will be presented that some classes of Riemannian 3symmetric spaces satisfy weakly symmetric property or not. This is joint work with L. Vanhecke and Y. Watanabe. Reference: J. Berndt and L. Vanhecke, Geometry of weakly symmetric spaces, J. Math. Sci. Japan, 48 (1996), 745–760. W. Ziller, Weakly symmetric spaces, Topics in Geometry: In Memory of Joseph D’Atri, S. Gindikin ed., Birkhäuser, Boston, 1996, pp.355–368.