The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor
Differential Geometry
2025-10-15 v1
Abstract
In this article, we give a new proof of a result due to J. Kim, which states that the Ricci tensor of a gradient Ricci soliton with dimension and harmonic Weyl tensor has at most three distinct eigenvalues. This result constitutes an essential step in the classification of such manifolds, originally established by J. Kim in dimension and subsequently extended to dimensions . Our proof offers two notable advantages: it is shorter and does not require the use of any specialized moving frame.
Cite
@article{arxiv.2510.11939,
title = {The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor},
author = {Valter Borges and Matheus Andrade Ribeiro de Moura Horácio and João Paulo dos Santos},
journal= {arXiv preprint arXiv:2510.11939},
year = {2025}
}