In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every h Î [-1,-frac2Ö{n-1}n)hin[-1,-frac{2sqrt{n-1}}{n}) can be realized as the constant curvature of a complete immersion of S1n-1×mathbbRS_1^{n-1}times mathbb{R} in the (n + 1)-dimensional de Sitter space S1n+1hbox{bf S}_1^{n+1}. We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and 5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.
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机译：在本文中，我们推广了Perdomo中给出的欧氏空间，球面和双曲线空间的超曲面的恒定平均曲率（CMC）浸入的显式公式（Asian J Math 14（1）：73-108，2010; Rev Colomb Mat 45（1） ）：81-96，2011）提供了具有恒定截面曲率的半黎曼流形中具有恒定平均曲率和非恒定主曲率的多个浸没族的显式示例。特别地，我们证明每个h∈[-1，-frac2Ö{n-1} n）hin [-1，-frac {2sqrt {n-1}} {n}）都可以实现为a的恒定曲率将S 1 n-1 ×mathbbRS_1 ^ {n-1}完全浸没在（n +1）维de Sitter空间S 1 n + 1 hbox {bf S} _1 ^ {n + 1}。我们在Minkowski空间提供3种类型的CMC浸入，在de Sitter空间提供5种类型的CMC浸入，在anti de Sitter空间提供5种类型的CMC浸入。在本文的最后，我们分析了可以扩展到封闭超曲面的示例族。
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