Complete maximal space-like hypersurfaces in an anti-de Sitter space of dimension 4 (Q1904461)

Let \(M^{u+ 1}_1(c)\) be a Lorentz space form. Any submanifold \(M\) of it is called spacelike if \(M\) inherits a positive definite metric from the ambient space. The present author gives here the Lorentz version in the anti-de Sitter space \(H^4_1(c)\) of Chern's problem [\textit{C.-K. Peng} and \textit{C.-L. Terng}, Seminar on minimal submanifolds, Ann. Math. Stud. 103, 177-198, (1983; Zbl 0534.53048)], [\textit{Q. Cheng}, Osaka J. Math. 27, No. 4, 885-892 (1990; Zbl 0735.53047)], [\textit{R. Aiyama} and \textit{Q. Cheng}, Kodai Math. J. 15, No. 3, 375-386 (1992; Zbl 0777.53058)]. The main theorem here gives the conditions under which a 3-dimensional complete maximal hypersurface with constant scalar curvature in \(H^4_1(c)\) is congruent to the hyperbolic cylinder \(H^1(c_1)\times H^2(c_2)\).