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Ricci-like Solitons with Arbitrary Potential and Gradient Almost Ricci-like Solitons on Sasaki-like Almost Contact B-metric Manifolds

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Abstract

Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. A manifold of this type can be considered as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. The soliton under study is characterized and proved that its Ricci tensor is equal to the vertical component of both B-metrics multiplied by a constant. Thus, the scalar curvatures with respect to both B-metrics are equal and constant. In the 3-dimensional case, it is found that the special sectional curvatures with respect to the structure are constant. Gradient almost Ricci-like solitons on Sasaki-like almost contact B-metric manifolds have been proved to have constant soliton coefficients. Explicit examples are provided of Lie groups as manifolds of dimensions 3 and 5 equipped with the structures under study.

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Funding

The author was supported by projects MU21-FMI-008 and FP21-FMI-002 of the Scientific Research Fund, University of Plovdiv Paisii Hilendarski, Bulgaria.

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Authors and Affiliations

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

    Mancho Manev

  2. Faculty of Pharmacy, Department of Medical Physics and Biophysics, Medical University–Plovdiv, 15A Vasil Aprilov Blvd, Plovdiv, 4002, Bulgaria

    Mancho Manev

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Manev, M. Ricci-like Solitons with Arbitrary Potential and Gradient Almost Ricci-like Solitons on Sasaki-like Almost Contact B-metric Manifolds. Results Math 77, 149 (2022). https://doi.org/10.1007/s00025-022-01704-6

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