ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: Primary 53C40: Secondary 53C42 Matsuyama, Yoshio, Department of Mathematics, Chuo Univ. Japan On totally real submanifolds in CP^{n}(c) We’d like to announce the following two characterizations of a totally real minimal submanifolds M^{n} in CP^{n}(c).

(1) If M^{n} has at most two principal curvatures in the direction of any normal, then M^{n} is isotropic, and M^{n} is totally geodesic or n = 2, 8, 14, 26.

(2) If M^{n} satisfies RA_{ξ} = 0 in the direction of any normal ξ, then M^{n} is isotropic, and M^{n} is totally geodesic or n = 2, 5, 8, 14, 26. References: S. Montiel, A. Ros and F. Urbano, Curvature pinching and eigenvalue rigidity for minimal submanifolds, Math. Z. 191 (1986), 537-548. S. Montiel and F. Urbano, Isotropic totally real submanifolds, Math. Z. 199(1988), 55-60.