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Totally complex submanifolds of the Cayley projective plane

Published online by Cambridge University Press:  18 May 2009

Liu Ximin
Liu Ximin
Affiliation:
Department of Mathematics, Nankai University, Tianjin 300071, P. R. China
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Abstract

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Let h be the second fundamental form of a compact submanifold M of the Cayley projective plane CaP2. We determine all compact totally complex submanifolds of complex dimension n in CaP2 satisfying |h|2 ≤ n.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 2 , May 1998 , pp. 161 - 166
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

1.Besse, A. L., Manifolds all of whose geodesies are closed (Springer-Verlag, Berlin, 1978).CrossRefGoogle Scholar
2.Brown, R. and Gray, A., Riemannian manifolds with holonomy group Spin (9), in Diff. Geom. in honor of K. Yano, 42–59 (Tokyo, 1972).Google Scholar
3.Coulton, P. and Gauchman, H., Submanifolds of quaternion projective space with bounded second fundamental form, Kodai Math. J. 12 (1989), 296–307.CrossRefGoogle Scholar
4.Coulton, P. and Glazebrook, J., Submanifolds of Cayley projective plane with bounded second fundamental form, Geom. Dedi. 33 (1990), 265–272.Google Scholar
5.Ros, A., Positively curved Kaehler submanifolds, Proc. Amer. Math. Soc. 93 (1985), 329–331.CrossRefGoogle Scholar
6.Ros, A., A characterization of seven compact Kaehler submanifolds by holomorphic pinching, Ann. of Math. 121 (1985), 377–382.CrossRefGoogle Scholar
7.Tsukada, K., Parallel submanifolds in a quaternion projective space, Osaka J. Math. 22 (1985), 187–241.Google Scholar