A classification of triharmonic hypersurfaces in a pseudo-Riemannian space form

Abstract

The purpose of this article is to investigate triharmonic hypersurfaces Mtn in a pseudo-Riemannian space form Nt1n+1(c). Assuming that the shape operator is diagonalizable, we show that every CMC triharmonic hypersurface either has constant scalar curvature or it is minimal if cε>0 and every CMC triharmonic hypersurface is minimal if cε<0, where ε is the inner product of the unit normal vector of Mtn. Furthermore, we prove that any CMC triharmonic hypersurface with diagonalizable shape operator in a pseudo-Euclidean space Et1n+1 is actually minimal provided that zero is a principal curvature of multiplicity at most one.