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Para-Sasaki-like Riemannian manifolds and new Einstein metrics

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Abstract

We determine a new class of paracontact paracomplex Riemannian manifolds derived from certain cone construction, called para-Sasaki-like Riemannian manifolds, and give explicit examples. We define a hyperbolic extension of a paraholomorphic paracomplex Riemannian manifold, which is a local product of two Riemannian spaces of equal dimension, and show that it is a para-Sasaki-like Riemannian manifold. If the original paraholomorphic paracomplex Riemannian manifold is a complete Einstein space of negative scalar curvature, then its hyperbolic extension is a complete Einstein para-Sasaki-like Riemannian manifold of negative scalar curvature. Thus, we present new examples of complete Einstein Riemannian manifolds of negative scalar curvature.

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Acknowledgements

The research of S.I. is partially supported by Contract DH/12/3/12.12.2017, Contract 80-10-161/05.04.2021 with the Sofia University “St. Kliment Ohridski” and the National Science Fund of Bulgaria, National Scientific Program “VIHREN”, Project no. KP-06-DV-7. The research of H. M. is partially supported by the National Scientific Program “Young Researchers and Post-Doctorants” and the project MU21-FMI-008 of the Scientific Research Fund, University of Plovdiv “Paisii Hilendarski”. The research of M. M. is partially supported by projects MU21-FMI-008 and FP21-FMI-002 of the Scientific Research Fund, University of Plovdiv “Paisii Hilendarski”.

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Authors and Affiliations

  1. Department of Geometry, Faculty of Mathematics and Informatics, St. Kliment Ohridski University of Sofia, 5 James Bourchier Blvd, 1164, Sofia, Bulgaria

    Stefan Ivanov

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    Stefan Ivanov

  3. Department of Medical Informatics, Biostatistics and e-Learning, Faculty of Public Health, Medical University of Plovdiv, 15A Vasil Aprilov Blvd, 4002, Plovdiv, Bulgaria

    Hristo Manev & Mancho Manev

  4. Department of Algebra and Geometry, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen St, 4000, Plovdiv, Bulgaria

    Mancho Manev

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  1. Stefan Ivanov
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  2. Hristo Manev
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  3. Mancho Manev
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Correspondence to Mancho Manev.

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Ivanov, S., Manev, H. & Manev, M. Para-Sasaki-like Riemannian manifolds and new Einstein metrics. RACSAM 115, 112 (2021). https://doi.org/10.1007/s13398-021-01053-z

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