Calculus of Variations and Geometric Measure Theory

H. D. Cao - G. Catino - Q. Chen - C. Mantegazza - L. Mazzieri

Bach-Flat Gradient Steady Ricci Solitons

created by catino on 24 Jul 2011
modified on 24 Jan 2014


Published Paper

Inserted: 24 jul 2011
Last Updated: 24 jan 2014

Journal: Calc. Var. Partial Differential Equations
Volume: 49
Number: 1-2
Pages: 125-138
Year: 2014


In this paper we prove that any $n$-dimensional ($n> 3$) complete Bach-flat gradient steady Ricci solitons 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.