Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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G. Catino - P. Mastrolia

Weyl scalars on compact Ricci solitons

created by catino on 17 Oct 2023



Inserted: 17 oct 2023
Last Updated: 17 oct 2023

Year: 2018

ArXiv: 1804.09424 PDF


We investigate the triviality of compact Ricci solitons under general scalar conditions involving the Weyl tensor. More precisely, we show that a compact Ricci soliton is Einstein if a generic linear combination of divergences of the Weyl tensor contracted with suitable covariant derivatives of the potential function vanishes. In particular we recover and improve all known related results. This paper can be thought as a first, preliminary step in a general program which aims at showing that Ricci solitons can be classified finding a "generic" $[k, s]$-vanishing condition on the Weyl tensor, for every $k, s\in\mathbb{N}$, where $k$ is the order of the covariant derivatives of Weyl and $s$ is the type of the (covariant) tensor involved.

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