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On product k-Chen submanifolds

Published online by Cambridge University Press:  18 May 2009

Uǧur Dursunf
Uǧur Dursunf
Affiliation:
School of Mathematics, The University of Leeds, Leeds LS2 9JT, England
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B. Rouxel [7] and S. J. Li and C. S. Houh [6] have generalised the notion of an -submanifold (Chen submanifold) to an k-submanifold. In [1] we have studied the relation between their definitions for the Euclidean case.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 3 , September 1997 , pp. 243 - 249
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

REFERENCES

1.Carter, S. and Dursun, U., On generalised Chen and it k-minimal immersions, Beiträge zue Algebra und Geometrie/Contributions to Algebra and Geometry, 38 (1) (1997), 125–134.Google Scholar
2.Chen, B.-Y., Geometry of submanifolds, (Marcel Dekker, New York, 1973).Google Scholar
3.Chen, B.-Y., Pseudo-umbilical submanifold of a Riemannian manifold of constant curvature II, J. Math. Soc. Japan 25 (1) (1973), 105–114.Google Scholar
4.Gheysens, L., Verheyen, P. and Verstraelen, L., Sur les surfaces ou les surfaces de Chen, C.R. Acad. Sc. Paris I 292 (1981), 913–916.Google Scholar
5.Gheysens, L., Verheyen, P. and Verstraelen, L., Characterization and examples of Chen submanifolds, J. Geometry 20 (1983), 47–62.Google Scholar
6.Li, S. J. and Houh, C. S., Generalized Chen submanifolds, J. Geometry 48 (1993), 144–156.CrossRefGoogle Scholar
7.Rouxel, B., -submanifolds in Euclidean space, Kodai Math. J. 4 (1981), 181–188.CrossRefGoogle Scholar
8.Simons, J., Minimal varieties in Riemannian manifolds, Ann. of Math. 88 (1968), 62–105.CrossRefGoogle Scholar