Geometric Characterizations of Riemann Solitons

Abdul Haseeb, Meraj Ali Khan, D. G. Prakasha and T. Manjula

Journal of Mathematics, 2026, vol. 2026, 1-10

Abstract: In this paper, we find the geometric characterizations of Riemann solitons within the background of co-Kähler manifolds admitting semisymmetric metric ζ-connection. Let g,V be a Riemann soliton on a co-Kähler manifold M admitting a semisymmetric metric ζ-connection. It shows that the soliton vector field V is a constant multiple of the vector field ζ. Furthermore, if V is collinear with ζ, then the manifold M becomes ϑ-Einstein. Moreover, it is established that if g,V is a Riemann soliton on M with the soliton vector field V having constant divergence, under the same connection, then M is Einstein, and the soliton is of shrinking type. Besides these, it is established that if g,V is a Riemann soliton on 3-dimensional co-Kähler manifold M3 admitting semisymmetric metric ζ-connection, then the soliton vector V is a Killing vector field and the manifold M3 is of constant curvature 1. Moreover, it has been shown that for the case of M3, an almost Riemann soliton reduces to Riemann soliton. Finally, we consider a co-Kähler manifold M admitting a gradient Riemann soliton with semisymmetric metric ζ-connection and proved that the manifold M is Einstein or the gradient function f is constant.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8684119

DOI: 10.1155/jom/8684119

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