ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53C42, 53C40 Ximin, Liu, Department of Mathematics, Dalian University of Technology, Dalian 116024, P. R. China Positively curved totally complex submanifolds in the Cayley projective space Let M be a compact totally complex submanifold of complex dimension 2 in the Cayley projective plane CaP^{2}. Denote by K the sectional curvature of M. In [2], it was proved that the compact totally complex submanifold M of complex dimension 2 in cayley projective plane CaP^{2} satisfying K > \frac{1}{8} is totally geodesic and M is CP^{2}. In the present paper we proved that if the sectional curvature K of M satisfies K > 0, then M is totally geodesic and M is CP^{2}. Ref. [1] P. Coulton, J. Glazebrook, Submanifolds of Cayley projective plane with bounded second fundamental form, Geom. Dedi. 33 (1990), 265–272.

[2] Liu Ximin, Totally complex submanifolds of the Cayley projective plane, Tsukuba J. Math. to appear. [3] K. Tsukada, Parallel submanifolds in a quaternion projective space, Osaka J. Math. 22 (1985), 187–241.