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\(\mathcal {D}-\)homothetic deformation on para-Sasaki-like Riemannian manifolds

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Abstract

The objective of this paper is to apply the notion of \(\mathcal {D}-\)ho-mothetic deformation to almost paracontact almost paracomplex Riemannian manifolds. In case the manifold is para-Sasaki-like, the relation between their Levi-Civita connections is given. It is shown that the \(\mathcal {D}-\)homothetic deformation of para-Einstein-like manifold and para-Ricci-like soliton is also a para-Einstein-like manifold and para-Ricci-like soliton, respectively. Moreover, if para-Sasaki-like manifold M admits a gradient almost Ricci-like soliton, it is investigated whether the \(\mathcal {D}-\)homothetic deformation of M admits a gradient Ricci-like soliton. Finally, it is given an example.

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Acknowledgements

The author would like to thank the referees for their valuable comments which helped to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Eskisehir Technical University, Yunus Emre Campus, Eskisehir, Turkey

    Şenay Bulut & Pınar İnselöz

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  1. Şenay Bulut
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  2. Pınar İnselöz
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All authors wrote the main manuscript tex and reviewed the manuscript.

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Correspondence to Şenay Bulut.

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Bulut, Ş., İnselöz, P. \(\mathcal {D}-\)homothetic deformation on para-Sasaki-like Riemannian manifolds. J. Geom. 114, 7 (2023). https://doi.org/10.1007/s00022-023-00668-4

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  • DOI: https://doi.org/10.1007/s00022-023-00668-4

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