On a Generalization of the Catenoid

Abstract

It is a classical result that the only surface of revolution in Euclidean space E 3 which is minimal is the catenoid. Of course the surface is conformally flat, but if M n , n ≧ 4, is a conformally flat hypersurface of Euclidean space En+1, then M n admits a distinguished direction [2] (“tangent to the meridians“). Thus we seek to characterize conformally flat hypersurfaces of E n+1 which are minimal. Specifically we prove the following THEOREM. Let M n , n ≧ 4, be a conformally flat, minimal hypersurface immersed in E n+1 .