Calculus of Variations and Geometric Measure Theory
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G. Catino - P. Mastrolia

Weyl scalars on compact Ricci solitons

created by catino on 25 Apr 2018
modified on 03 Nov 2018


Accepted Paper

Inserted: 25 apr 2018
Last Updated: 3 nov 2018

Journal: J. Geom. Anal.
Year: 2018


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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