The Evolution of the Weyl Tensor under the Ricci Flow
[L’évolution du tenseur de Weyl d’une variété par le flot de Ricci]
Catino, Giovanni1 ; Mantegazza, Carlo2
1 SISSA International School for Advanced Studies Via Bonomea 265 Trieste 34136 (Italy)
2 Scuola Normale Superiore di Pisa P.za Cavalieri 7 Pisa 56126 (Italy)
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1407-1435.

Nous calculons l’équation d’évolution du tenseur de Weyl d’une variété riemannienne par le flot de Ricci et nous discutons des conséquences pour la classification des solitons de Ricci localement conformément plats.

We compute the evolution equation of the Weyl tensor under the Ricci flow of a Riemannian manifold and we discuss some consequences for the classification of locally conformally flat Ricci solitons.

DOI : 10.5802/aif.2644
Classification : 53C21, 53C25
Keywords: Ricci solitons, singularity of Ricci flow
Mot clés : solitons de Ricci, singularités du flot de Ricci
Catino, Giovanni 1 ; Mantegazza, Carlo 2

1 SISSA International School for Advanced Studies Via Bonomea 265 Trieste 34136 (Italy)
2 Scuola Normale Superiore di Pisa P.za Cavalieri 7 Pisa 56126 (Italy) 
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Catino, Giovanni; Mantegazza, Carlo. The Evolution of the Weyl Tensor under the Ricci Flow. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1407-1435. doi : 10.5802/aif.2644. http://www.numdam.org/articles/10.5802/aif.2644/

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