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Totally real pseudo-umbilical submanifolds of a quaternion space form

Published online by Cambridge University Press:  18 May 2009

Huafei Sun
Huafei Sun
Affiliation:
Department of MathematicsTokyo Metropolitan UniversityHachioji, Tokyo, 192-03, Japan
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Let M(c) denote a 4n-dimensional quaternion space form of quaternion sectional curvature c, and let P(H) denote the 4n-dimensional quaternion projective space of constant quaternion sectional curvature 4. Let N be an n-dimensional Riemannian manifold isometrically immersed in M(c). We call N a totally real submanifold of M(c) if each tangent 2-plane of N is mapped into a totally real plane in M (c). B. Y. Chen and C. S. Houh proved in [1].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 1 , March 1998 , pp. 109 - 115
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

REFERENCES

1.Chen, B. Y. and Houh, C. S., Totally real submanifolds of a quaternion projective space, Ann. di Math. Pura Appl. 120 (1979), 185–199.CrossRefGoogle Scholar
2.Chen, B. Y., Some results of Chern-do Carmo-Kobayashi type and the length of second fundamental form, Indiana Univ. Math. J. 20 (1971), 1175–1185.CrossRefGoogle Scholar
3.Chern, S. S., do Carmo, M. and Kobayashi, S., Minimal submanifolds of a sphere with second fundamental form of constant length, in Functional Analysis and Related Field (Springer-Verlag, New York, 1970) p. 60–75.Google Scholar
4.Li, A. M. and Li, J. M., An intrinsic rigidity theorem for minimal submanifolds in a sphere, Arch. Math. 58 (1992), 582–594.Google Scholar