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 ∈ N, where k is the order of the covariant derivatives of Weyl and s is the type of the (covariant) tensor involved.

Weyl Scalars on Compact Ricci Solitons / G. Catino, P. Mastrolia. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 29:4(2019 Dec), pp. 3328-3344. [10.1007/s12220-018-00120-z]

Weyl Scalars on Compact Ricci Solitons

P. Mastrolia
Ultimo
2019

Abstract

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 ∈ N, where k is the order of the covariant derivatives of Weyl and s is the type of the (covariant) tensor involved.
Ricci solitons; Triviality results; Weyl tensor; Weyl scalars
Settore MAT/03 - Geometria
dic-2019
13-nov-2018
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/602082
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