Abstract
The object of the offering article is to investigate an almost Riemann soliton and a gradient almost Riemann soliton in a non-cosymplectic normal almost contact metric manifold \(M^3\). Before all else, it is proved that if the metric of \(M^3\) is a Riemann soliton with divergence-free potential vector field Z, then the manifold is quasi-Sasakian and is of constant sectional curvature -\(\lambda \), provided \(\alpha ,\beta =\) constant. Also, it is shown that if the metric of \(M^3\) is an almost Riemann Soliton and Z is pointwise collinear with \(\xi \) and has constant divergence, then Z is a constant multiple of \(\xi \) and the almost Riemann Soliton reduces to a Riemann soliton, provided \(\alpha ,\;\beta =\)constant. Additionally, it is established that if \(M^3\) with \(\alpha ,\; \beta =\) constant admits a gradient almost Riemann soliton \((\gamma ,\xi ,\lambda )\), then the manifold is either quasi-Sasakian or is of constant sectional curvature \(-(\alpha ^2-\beta ^2)\). Finally, we develop an example of \(M^3\) admitting a Riemann soliton.
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De, K., De, U.C. A note on almost Riemann Solitons and gradient almost Riemann Solitons. Afr. Mat. 33, 74 (2022). https://doi.org/10.1007/s13370-022-01010-y
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DOI: https://doi.org/10.1007/s13370-022-01010-y
Keywords
- 3-dimensional normal almost contact metric manifold
- Almost Riemann soliton
- Gradient almost Riemann soliton