We generalized the lower bound estimates for eigenvalues of the Dirac operator on spacelike hypersurfaces of Lorentzian manifolds obtained by Yongfa Chen in (Sci China Ser A Math 52(11):2459–2468, 2009) based on the constraint between the scalar curvature of the manifold, energy–momentum tensor and the mean curvature of the manifold. Afterwards, we examined the geometric data in the case of estimation satisfies equality condition.

中文翻译：

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洛伦兹流形类空间自旋超曲面的一些估计

我们在 (Sci China Ser A Math 52(11):2459–2468, 2009) 基于流形、能量-动量张量和流形的平均曲率。然后，我们在估计满足相等条件的情况下检查几何数据。