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In this paper, we take a look at conditions that make a Riemann soliton trivial, compacity being one of them. We also obtain scalar curvature estimates for complete shrinking or steady gradient Riemann solitons whose scalar curvature is bounded from below at infinity. [ABSTRACT FROM AUTHOR]

Generalized quasi-conformal curvature tensor (ω-tensor) has the flavor of conformal, conharmonic, concircular, projective, m-projective, W1-curvature, W2-curvature and W4-curvature tensors. In the present paper we have investigated the nature of Riemann solitons in α-cosymplectic manifold in the light of generalized weakly ω-symmetric structure.

We consider almost Riemann solitons (V , λ) in a Riemannian manifold and underline their relation to almost Ricci solitons. When V is of gradient type, using Bochner formula, we explicitly express the function λ by means of the gradient vector field V and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential vector field of the soliton is solenoidal or torse-forming, with a special view towards curvature. [ABSTRACT FROM AUTHOR]

The object of the present study is to investigate the nature of Riemann solitons for hyper generalized pseudo symmetric generelized D-conformally deformed Kenmotsu manifold. [ABSTRACT FROM AUTHOR]