https://neckpinch.com/authors/fengyuan-zhang/New arXiv papers by Fengyuan Zhang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.12930/arxiv:2610.12930Fri, 09 Oct 2026 00:00:00 GMTFengyuan Zhang — We give direct proofs of rigidity results for gradient Ricci solitons, compact quasi-Einstein manifolds with boundary, and critical spaces with cyclic parallel Ricci tensor. For solitons and quasi-Einstein manifolds, successive traces of first-order pointwise identities yield quadratic equations for the Ricci tensor and its modification. These equations imply radial flatness and radial Q-flatness, respectively, and the corresponding global rigidity theorems apply. For critical spaces, comparison of two expressions for the Laplacian of the Hessian gives a pointwise tensor identity whose scalar contraction yields a weighted divergence formula. Integration then gives the vacuum static, CPE, and Miao–Tam conclusions. The same comparison also proves Ricci parallelism pointwise for solitons and quasi-Einstein manifolds.Ricci solitonsEinstein metricsAlmost & η-Ricci solitonsStability & uniquenessBoundaries & non-compact https://neckpinch.com/papers/2608.21732/arxiv:2608.21732Sat, 22 Aug 2026 00:00:00 GMTFengyuan Zhang — The aim of this paper is to classify some special Riemannian manifolds with cyclic parallel Ricci tensor, i.e. \beginequation D_ijk=\nabla_iR_jk+\nabla_jR_ki+\nabla_kR_ij=0\nonumber \endequation These structures include non-compact gradient shrinking Ricci soliton, compact (m > 1)-quasi-Einstein manifolds with boundary and critical spaces. We will construct some integral identities and make use of the curvature conditions reasonably to prove that the Ricci tensor is parallel.Ricci solitonsEinstein metricsAlmost & η-Ricci solitonsBoundaries & non-compact