https://neckpinch.com/authors/dario-daniele-monticelli/New arXiv papers by Dario Daniele Monticelli, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1602.00534/arxiv:1602.00534Mon, 01 Feb 2016 00:00:00 GMTGiovanni Catino, Paolo Mastrolia, Dario Daniele Monticelli — We classify complete gradient Ricci solitons satisfying a fourth-order vanishing condition on the Weyl tensor, improving previously known results. More precisely, we show that any n-dimensional (n≥ 4) gradient shrinking Ricci soliton with fourth order divergence-free Weyl tensor is either Einstein, or a finite quotient of N^(n-k)× ℝ^k, (k > 0), the product of a Einstein manifold N^(n-k) with the Gaussian shrinking soliton ℝ^k. The technique applies also to the steady and expanding cases in all dimensions. In particular, we prove that a three dimensional gradient steady soliton with third order divergence-free Cotton tensor, i.e. with vanishing double divergence of the Bach tensor, is either flat or isometric to the Bryant soliton.Ricci solitonsAncient solutionsEinstein metrics3-manifolds