https://neckpinch.com/authors/mijia-lai/New arXiv papers by Mijia Lai, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.17691/arxiv:2610.17691Tue, 13 Oct 2026 00:00:00 GMTMijia Lai, Guoqiang Wu — We prove two constant rank theorems for the Ricci tensor in two geometric settings: manifolds with harmonic curvature and gradient Ricci solitons. In both cases, if the k-intermediate Ricci curvature satisfies Ricₖ≥0 for some 1≤ k≤ n-2, then the Ricci tensor has constant rank and its nullity distribution is parallel. In the complete case, the universal cover splits isometrically along the Ricci-null directions. We also show that the range 1≤ k≤ n-2 is sharp: in every dimension n≥4, nonnegative Ricci curvature alone does not imply the constant rank property in either setting.Ricci solitons