A classification of certain 3-dimensional conformally flat Euclidean hypersurfaces

Oscar J. Garay

Vol. 162 (1994), No. 1, 13–25

DOI: 10.2140/pjm.1994.162.13

Abstract

This paper deals with conformally flat hypersurfaces of the 4-dimensional Euclidean space E⁴. We classify those conformally flat hypersurfaces of E⁴ whose mean curvature vector, H, is an eigenvector of their Laplacian i.e. ΔH = λH; λ ∈ R.

The classification is done by proving that the classical Cartan-Schouten result remains valid for this kind of hypersurfaces.

Mathematical Subject Classification 2000

Primary: 53C40

Secondary: 53C21

Milestones

Received: 3 February 1992

Revised: 20 November 1992

Published: 1 January 1994