Hypersurfaces in non-flat Lorentzian space forms satisfying \(L_k \psi = a\psi + b\) (Q439212)

Let \(\mathbb M_c^{n+1}\) be either the De Sitter space \(\mathbb S_1^{n+1}\subset\mathbb R_1^{n+2}\) if \(c=1\), or the anti De Sitter space \(\mathbb H_1^{n+1}\subset\mathbb R_2^{n+2}\) if \(c=-1\). In the reviewed paper the authors study orientable hypersurfaces \(M\) immersed into \(\mathbb M_c^{n+1}\) whose position vector \(\psi\) satisfies the condition \(L_k\psi=A\psi+b\) for some constant matrix \(A\in\mathbb R^{(n+2)\times(n+2)}\) and some vector \(b\in\mathbb R_q^{n+2}\), where \(L_k\) is the linearized operator of the \((k+1)\)-th mean curvature of \(M\).NEWLINENEWLINEThe authors give two classification results. First in the case when \(A\) is self adjoint and \(b=0\), and next in the case when the k-th mean curvature \(H_k\) of \(M\) is constant, \(A\) is self-adjoint and \(b\) is non-zero.