• 대한수학회논문집
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• 제38권4호
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• pp.1215-1231
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• 2023

The present article contains the study of D-homothetically deformed f-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.

• 대한수학회논문집
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• 제38권3호
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• pp.881-892
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• 2023

In this paper, we study almost cosymplectic manifolds with nullity distributions admitting Riemann solitons and gradient almost Riemann solitons. First, we consider Riemann soliton on (κ, µ)-almost cosymplectic manifold M with κ < 0 and we show that the soliton is expanding with ${\lambda}{\frac{\kappa}{2n-1}}(4n - 1)$ and M is locally isometric to the Lie group G_ρ. Finally, we prove the non-existence of gradient almost Riemann soliton on a (κ, µ)-almost cosymplectic manifold of dimension greater than 3 with κ < 0.