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Ricci-Like Solitons with Vertical Potential on Sasaki-Like Almost Contact B-Metric Manifolds

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Abstract

Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case, the properties for a parallel or recurrent Ricci-tensor are studied. In the latter case, it is shown that the potential of the considered Ricci-like soliton has a constant length and the manifold is \(\eta \)-Einstein. Other curvature conditions are also found, which imply that the main metric is Einstein. After that, some results are obtained for a parallel symmetric second-order covariant tensor on the manifolds under study. Finally, an explicit example of dimension 5 is given and some of the results are illustrated.

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Acknowledgements

The author was supported by the Medical University of Plovdiv and the Projects MU19-FMI-020 and FP19-FMI-002 of the Scientific Research Fund, University of Plovdiv Paisii Hilendarski, Bulgaria.

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Authors and Affiliations

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

    Mancho Manev

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

    Mancho Manev

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  1. Mancho Manev
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Correspondence to Mancho Manev.

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Dedicated to the memory of Prof. Heinrich Wefelscheid

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Manev, M. Ricci-Like Solitons with Vertical Potential on Sasaki-Like Almost Contact B-Metric Manifolds. Results Math 75, 136 (2020). https://doi.org/10.1007/s00025-020-01267-4

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