Year: 2025
Type: article
Abstract: The aim of this work is to examine Ricci solitons, which are among the popular research topics of differential geometry nowadays, by focusing on the 4-dimensional case. In this respect, 4-dimensional manifolds admitting different metric signatures are considered by expanding the studies in the literature. Several examples of Ricci solitons are given for 4-dimensional manifolds with Lorentz or neutral metric signatures. In the case of the manifold containing a parallel vector field, its relationship with the potential field is investigated and steady Ricci solitons are obtained under certain conditions. A similar analysis is made for recurrent vector fields. More explicitly, an example of a Ricci soliton whose potential field is recurrent is found and the Segre type of the Ricci tensor is determined. The results in question are interpreted by associating them with concepts such as holonomy theory and other types of vector fields on the relevant manifolds.
DOI: 10.66899/40c2244a
Authors: Bahar Kirik Rácz, Burcu Cindik
Institution: Marmara University
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7166327925
FWCI:
Cites:
Cited by:
Related to: