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On a Generalization of the Catenoid

Published online by Cambridge University Press:  20 November 2018

David E. Blair
David E. Blair*
Affiliation:
Michigan State University, East Lansing, Michigan
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It is a classical result that the only surface of revolution in Euclidean space E3 which is minimal is the catenoid. Of course the surface is conformally flat, but if Mn, n ≧ 4, is a conformally flat hypersurface of Euclidean space En+1, then Mn admits a distinguished direction [2] (“tangent to the meridians“). Thus we seek to characterize conformally flat hypersurfaces of En+1 which are minimal. Specifically we prove the following

THEOREM. Let Mn, n ≧ 4, be a conformally flat, minimal hypersurface immersed in En+1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 231 - 236
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Chen, B.-Y., Geometry of submanifolds (Marcel-Dekker, Inc., New York, 1973).Google Scholar
2. Chen, B.-Y. and Yano, K., Conformally flat submanifolds (to appear).Google Scholar