On \(\eta\)-biharmonic hypersurfaces in pseudo-Riemannian space forms
An \(\eta\)-biharmonic submanifold is an isometric immersion \(\phi: (M^m, g)\to (N,h)\) which is a critical point of the linear combination \(E_2(\phi)+\eta E_1(\phi)\) of the energy and the bienergy functionals. The equation for an \(\eta\)-biharmonic submanifold can be described as: \(\tau_1(\phi)=m\eta H\), where \(H\) is the mean curvature and \(\tau_2(\phi)\) is the bitension field of the submanifold. The paper under review studies \(\eta\)-biharmonic hypersurfaces with constant scalar curvature in 5-dimensional pseudo-Riemannian space forms. Among other things, the authors of the paper proved that if the shape operator of such hypersurface is diagonalizable, then the \(\eta\)-biharmonic hypersurface has constant mean curvature. Some partial classification of such hypersurfaces are also given.
scientific article; zbMATH DE number 7604041
scientific article