We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.

中文翻译：

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具有洛伦兹流形的封闭索具的零超曲面上的类 Chen 不等式

我们研究了洛伦兹流形的零超曲面，该超曲面具有封闭的索具。我们推导了涉及 Ricci 张量、标量曲率、平方平均曲率的不等式，用于具有洛伦兹空间形式的封闭索具的零超曲面和洛伦兹流形的屏幕同位零超曲面。我们还为洛伦兹流形的屏幕同位零超曲面建立了一个广义的 Chen-Ricci 不等式，该超曲面具有一个封闭的索具。