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

Abstract

We consider almost Riemann solitons $(V,\lambda )$ 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 $\lambda$ 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.

References in corpus (1)

• Riemann solitons and almost Riemann solitons on almost Kenmotsu manifolds

Cited by in corpus (2)

• Rigidity results for Riemann solitons
• Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds