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Gradient Ricci solitons and Fischer–Marsden equation on cosymplectic manifolds

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The goal of this paper is to investigate the existence of non-trivial solutions for Fischer–Marsden equation (FME) within the framework of \((2n+1)\)-dimensional cosymplectic manifolds. It is shown that the existence of such a solution forces the metric to be a gradient \(\eta \)-Ricci soliton. We also explore the geometrical properties of gradient Ricci solitons on \(\eta \)-Einstein cosymplectic manifolds.

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Acknowledgements

G.-E. Vîlcu was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI - UEFISCDI, project number PN-III-P4-ID-PCE-2020-0025, within PNCDI III.

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Author notes

  1. Sudhakar K. Chaubey and Gabriel-Eduard Vîlcu contributed equally to this work.

Authors and Affiliations

  1. Department of Information Technology, University of Technology and Applied Sciences Shinas, Al-Aqur, Shinas, 324, Oman

    Sudhakar K. Chaubey

  2. Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independenţei 313, Bucharest, 060042, Romania

    Gabriel-Eduard Vîlcu

  3. “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie Nr. 13, Bucharest, 050711, Romania

    Gabriel-Eduard Vîlcu

  4. Research Center in Geometry, Topology and Algebra, Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, Bucharest, 010014, Romania

    Gabriel-Eduard Vîlcu

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  1. Sudhakar K. Chaubey
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Correspondence to Gabriel-Eduard Vîlcu.

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Chaubey, S.K., Vîlcu, GE. Gradient Ricci solitons and Fischer–Marsden equation on cosymplectic manifolds. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 186 (2022). https://doi.org/10.1007/s13398-022-01325-2

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