Bach-flat gradient steady Ricci solitons |
| |
Authors: | Huai-Dong Cao Giovanni Catino Qiang Chen Carlo Mantegazza Lorenzo Mazzieri |
| |
Institution: | 1. Department of Mathematics, Lehigh University, Bethlehem, PA, 18015, USA 2. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy 3. Scuola Normale Superiore di Pisa, P.za Cavalieri 7, 56126, Pisa, Italy
|
| |
Abstract: | In this paper we prove that any n-dimensional (n ≥ 4) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant soliton. In particular, these results improve the corresponding classification theorems for complete locally conformally flat gradient steady Ricci solitons in Cao and Chen (Trans Am Math Soc 364:2377–2391, 2012) and Catino and Mantegazza (Ann Inst Fourier 61(4):1407–1435, 2011). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|