On some 3-dimensional almost η-Ricci solitons with diagonal metrics

2024/06/18 by Adara M. Blaga, Blaga, Adara M.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2406.12533

openalex publication_date 2024/06/18 · openalex created_date 2024/06/20 · openalex updated_date 2026/07/28

Abstract

We study some properties of a 3-dimensional manifold with a diagonal Riemannian metric as an almost η-Ricci soliton from the following points of view: under certain assumptions, we determine the potential vector field if η 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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