Geodesic
Riemann solitons on almost co-Kähler manifolds
Filomat, Tome 36 (2022) no. 4, p. 1403

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DOI

The aim of the present paper is to characterize almost co-Kähler manifolds whose metrics are the Riemann solitons. At first we provide a necessary and sufficient condition for the metric of a 3-dimensional manifold to be Riemann soliton. Next it is proved that if the metric of an almost co-Kähler manifold is a Riemann soliton with the soliton vector field ξ, then the manifold is flat. It is also shown that if the metric of a (κ, µ)-almost co-Kähler manifold with κ 0 is a Riemann soliton, then the soliton is expanding and κ, µ, λ satisfies a relation. We also prove that there does not exist gradient almost Riemann solitons on (κ, µ)-almost co-Kähler manifolds with κ 0. Finally, the existence of a Riemann soliton on a three dimensional almost co-Kähler manifold is ensured by a proper example
DOI : 10.2298/FIL2204403B
Classification : 53C25, 53C15
Keywords: Riemann flow, Riemann solitons, Almost co-Kähler manifolds, (κ, µ)-almost co-Kähler manifolds 
Gour Gopal Biswas; Xiaomin Chen; Uday C; and De. Riemann solitons on almost co-Kähler manifolds. Filomat, Tome 36 (2022) no. 4, p. 1403 . doi: 10.2298/FIL2204403B
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     title = {Riemann solitons on almost {co-K\"ahler} manifolds},
     journal = {Filomat},
     pages = {1403 },
     year = {2022},
     volume = {36},
     number = {4},
     doi = {10.2298/FIL2204403B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2204403B/}
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