We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k<n$, $A$ is a constant matrix and $b$ is a constant vector.
We show that the only hypersurfaces satisfying that condition are hypersurfaces with zero $H_{k+1}$ and constant $H_k$ ( when $cneq 0$ ), open pieces of totally umbilic hypersurfaces and open pieces of the standard Riemannian product of two totally umbilic hypersurfaces.
Pashaie, F., Kashani, S. (2013). Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b. Bulletin of the Iranian Mathematical Society, 39(1), 205-223.
MLA
F. Pashaie; S.M.B. Kashani. "Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b". Bulletin of the Iranian Mathematical Society, 39, 1, 2013, 205-223.
HARVARD
Pashaie, F., Kashani, S. (2013). 'Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b', Bulletin of the Iranian Mathematical Society, 39(1), pp. 205-223.
VANCOUVER
Pashaie, F., Kashani, S. Spacelike hypersurfaces in Riemannian or Lorentzian space forms satisfying L_k(x)=Ax+b. Bulletin of the Iranian Mathematical Society, 2013; 39(1): 205-223.
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