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Totally umbilical submanifolds of quaternion-space-forms

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  09 April 2009

Bang-Yen Chen
Bang-Yen Chen
Affiliation:
Department of Mathematics Michigan State University East Lansing, MI 48824
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Abstract

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Totally umbilical submanifolds of dimension greater than four in quaternion-space-forms are completely classified.

MSC classification

Secondary: 53B25: Local submanifolds 53C40: Global submanifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 2 , September 1978 , pp. 154 - 162
Copyright
Copyright © Australian Mathematical Society 1978

References

Cartan, E. (1946), Leçons sur la Géométrie des Espaces de Riemann (Gauthier-Villars, Paris, 2nd ed.).Google Scholar
Chen, B. Y. (1973), Geometry of Submanifolds (M. Dekkers, New York).Google Scholar
Chen, B. Y. (1977), “Totally umbilical submanifolds of Cayley plane”, Soochow J. Math. Natur. Sci. 3, 1–7.Google Scholar
Chen, B. Y. and Ogiue, K. (1974), “Two theorems on Kaehler manifolds”, Michigan Math. J. 21, 225–229.Google Scholar
Ishihara, S. (1974), “Quaternion Kaehlerian manifolds”, J. Differential Geometry 9, 483–500.CrossRefGoogle Scholar