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The aim of the present paper is to characterize almost co-K?hler 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-K?hler manifold is a Riemann soliton with the soliton vector field ?, then the manifold is flat. It is also shown that if the metric of a (?, ?)-almost co-K?hler manifold with ? < 0 is a Riemann soliton, then the soliton is expanding and ?, ?, ? satisfies a relation. We also prove that there does not exist gradient almost Riemann solitons on (?, ?)-almost co-K?hler manifolds with ? < 0. Finally, the existence of a Riemann soliton on a three dimensional almost co-K?hler manifold is ensured by a proper example.
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Gour Gopal Biswas
Xiaomin Chen
Uday Chand De
Filomat
China University of Petroleum, Beijing
University of Calcutta
University of Kalyani
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Biswas et al. (Sat,) studied this question.
www.synapsesocial.com/papers/69e30f6f35f394de16a46eb4 — DOI: https://doi.org/10.2298/fil2204403b