On some $3$-dimensional almost $\eta$-Ricci solitons with diagonal metrics

Adara M. Blaga

On some $3$-dimensional almost $\eta$-Ricci solitons with diagonal metrics

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arxiv 2406.12533 v3 pith:EBKJTD6D submitted 2024-06-18 math.DG

Adara M. Blaga This is my paper · ORCID

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keywords fieldpotentialvectoralmostdiagonaldimensionalmanifoldmetric

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abstract

We study some properties of a $3$-dimensional manifold with a diagonal Riemannian metric as an almost $\eta$-Ricci soliton from the following points of view: under certain assumptions, we determine the potential vector field if $\eta$ is given; we get constraints on the metric when the potential vector field has a particular expression; we compute the defining functions of the soliton when both the potential vector field and the $1$-form are prescribed. Moreover, we find conditions for the manifold to be flat. Based on the theoretical results, we provide examples.

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Constructing Ricci vector fields on $\mathbb R^2$ with a diagonal metric
math.DG 2025-01 conditional novelty 4.0 of 10

For diagonal metrics on R^2, the paper derives and solves the equations ∇V = Q, giving explicit Ricci vector fields and classifying them under certain separability assumptions.

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