A note on locally conformally flat gradient Ricci solitons

作者：Fernandez Lopez Manuel; Garcia Rio Eduardo^*

来源：Geometriae Dedicata, 2014, 168(1): 1-7.

DOI：10.1007/s10711-012-9815-0

• Gradient Ricci soliton
• Conformally flat
• Weyl tensor
• Warped product

We show that locally conformally flat gradient Ricci solitons, possibly incomplete, are locally isometric to a warped product of an interval and a space form. Consequently, we get that complete gradient shrinking and steady Ricci solitons with vanishing Weyl tensor are rotationally symmetric, from which their classification follows.

• 出版日期2014-2