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International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 1, Pages 197-200
http://dx.doi.org/10.1155/S0161171294000281

CR-hypersurfaces of the six-dimensional sphere

Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 23 July 1992

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We proved that there does not exist a proper CR-hypersurface of S6 with parallel second fundamental form. As a result of this we showed that S6 does not admit a proper CR-totally umbilical hypersurface. We also proved that an Einstein proper CR-hypersurface of S6 is an extrinsic sphere.