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Hypersurfaces with special quadric representations

Published online by Cambridge University Press:  17 April 2009

Lu Jitan
Lu Jitan
Affiliation:
Division of Mathematics, School of Science, National Institute of Education, Nanyang Technological University, Singapore 259756, e-mail: 95sd2363833u@acadzl.NTU.edu.sg
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Abstract

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Let x: Mn → Em be an isometric immersion of an n-dimensional Riemannian manifold into the m-dimensional Euclidean space. Then the map (where t denotes transpose) is called the quadric representation of Mn. In this paper, we study and classify hypersurfaces in the Euclidean space Em which satisfy , where B and C are two constant matrices, and Δ is the Laplacian operator of Mn. Some classification results are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 2 , October 1997 , pp. 227 - 234
Copyright
Copyright © Australian Mathematical Society 1997

References

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