On rotationally invariant shrinking Ricci solitons

Brett Kotschwar
2008 Pacific Journal of Mathematics  
We study the gradient Ricci shrinking soliton equation on rotationally symmetric manifolds of dimensions n ≥ 3 and prove that the only complete metrics on S n , ‫ޒ‬ n , and ‫ޒ‬ × S n−1 that admit shrinking soliton structures are respectively the round, flat, and standard cylindrical metrics.
doi:10.2140/pjm.2008.236.73 fatcat:g67nbwlelvazjaj6gq343bxl3u