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.
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.
Keywords: Ricci solitons, singularity of Ricci flow
Mot clés : solitons de Ricci, singularités du flot de Ricci
@article{AIF_2011__61_4_1407_0, author = {Catino, Giovanni and Mantegazza, Carlo}, title = {The {Evolution} of the {Weyl} {Tensor} under the {Ricci} {Flow}}, journal = {Annales de l'Institut Fourier}, pages = {1407--1435}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {4}, year = {2011}, doi = {10.5802/aif.2644}, zbl = {1255.53034}, mrnumber = {2951497}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2644/} }
TY - JOUR AU - Catino, Giovanni AU - Mantegazza, Carlo TI - The Evolution of the Weyl Tensor under the Ricci Flow JO - Annales de l'Institut Fourier PY - 2011 SP - 1407 EP - 1435 VL - 61 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2644/ DO - 10.5802/aif.2644 LA - en ID - AIF_2011__61_4_1407_0 ER -
%0 Journal Article %A Catino, Giovanni %A Mantegazza, Carlo %T The Evolution of the Weyl Tensor under the Ricci Flow %J Annales de l'Institut Fourier %D 2011 %P 1407-1435 %V 61 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2644/ %R 10.5802/aif.2644 %G en %F AIF_2011__61_4_1407_0
Catino, Giovanni; Mantegazza, Carlo. The Evolution of the Weyl Tensor under the Ricci Flow. Annales de l'Institut Fourier, Volume 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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