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arXiv · 2510.11939

The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor

Valter Borges·Matheus Andrade Ribeiro de Moura Horácio·João Paulo dos Santos
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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 $n \geq 4$ 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 $4$ and subsequently extended to dimensions $n\geq5$. Our proof offers two notable advantages: it is shorter and does not require the use of any specialized moving frame.

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Valter Borges, Matheus Andrade Ribeiro de Moura Horácio, João Paulo dos Santos. 2025-10-13. The Ricci tensor of a gradient Ricci soliton with harmonic Weyl tensor. https://arxiv.org/abs/2510.11939

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