부산대학교 도서관

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 [Formula omitted], where k is the order of the covariant derivatives of Weyl and s is the type of the (covariant) tensor involved.
Author(s): G. Catino [sup.1], P. Mastrolia [sup.2] Author Affiliations: (1) grid.4643.5, 0000 0004 1937 0327, Politecnico di Milano, , Milan, Italy (2) grid.4708.b, 0000 0004 1757 2822, Università degli Studi [...]