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The almost Schur Lemma in quaternionic contact geometry

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Abstract

We establish quaternionic contact (qc) versions of the so called Almost Schur Lemma, which give estimations of the qc scalar curvature on a compact qc manifold to be a constant in terms of the norm of the \([-1]\)-component and the norm of the trace-free part of the [3]-component of the horizontal qc Ricci tensor and the torsion endomorphism, under certain positivity conditions.

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Acknowledgements

The research of both authors is partially supported by Contract 80-10-163/23.05.2022 with the Sofia University “St. Kliment Ohridski”, and the National Science Fund of Bulgaria, National Scientific Program “VIHREN”, Project No. KP-06-DV-7. A. P. also acknowledges the University of Miami (UM), during his stay in which as a Fulbright Scholar under the auspices of the UM’s agreement with Fulbright Bulgaria, the final version of the manuscript was prepared.

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  1. University of Sofia, Faculty of Mathematics and Informatics, blvd. James Bourchier 5, 1164, Sofia, Bulgaria

    Stefan Ivanov & Alexander Petkov

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefan Ivanov

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  1. Stefan Ivanov
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  2. Alexander Petkov
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Correspondence to Alexander Petkov.

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Ivanov, S., Petkov, A. The almost Schur Lemma in quaternionic contact geometry. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 77 (2023). https://doi.org/10.1007/s13398-023-01403-z

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