Geodesic
On a Generalization of the Catenoid
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 231-236

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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 followingTHEOREM. Let Mn, n ≧ 4, be a conformally flat, minimal hypersurface immersed in En+1. 
Blair, David E. On a Generalization of the Catenoid. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 231-236. doi: 10.4153/CJM-1975-028-8
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[1] 1. Chen, B.-Y., Geometry of submanifolds (Marcel-Dekker, Inc., New York, 1973). Google Scholar

[2] 2. Chen, B.-Y. and Yano, K., Conformally flat submanifolds (to appear). Google Scholar

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