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arXiv · 2008.06413

Remarks on almost Riemann solitons with gradient or torse-forming vector field

Adara M. Blaga
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Abstract

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.

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Adara M. Blaga. 2021-01-15. Remarks on almost Riemann solitons with gradient or torse-forming vector field. https://doi.org/10.1007/s40840-021-01108-9

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