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Some Estimates Over Spacelike Spin Hypersurfaces of Lorentzian Manifold

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Abstract

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.

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Acknowledgements

This study was supported by TUBITAK The Scientific and Technological Research Council of Turkey (Project Number: 120F109). Also, The authors would like to appreciate TUBITAK (The Scientific and Technological Research Council of Turkey) for supporting this research.

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  1. Department of Mathematics, Ağrı İbrahim Çeçen University, Ağrı, Turkey

    Serhan Eker

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  1. Serhan Eker
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The authors declare that they have no conflict of interest. Also, they confirm that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Communicated by Jayme Vaz.

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Eker, S. Some Estimates Over Spacelike Spin Hypersurfaces of Lorentzian Manifold. Adv. Appl. Clifford Algebras 32, 13 (2022). https://doi.org/10.1007/s00006-022-01201-7

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