https://neckpinch.com/authors/jongsu-kim/New arXiv papers by Jongsu Kim, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2307.12243/arxiv:2307.12243Sun, 23 Jul 2023 00:00:00 GMTJongsu Kim — We make classifications of gradient Ricci solitons (M, g, f) with harmonic Weyl curvature. As a local classification, we prove that the soliton metric g is locally isometric to one of the following four types: an Einstein manifold, the Riemannian product of a Ricci flat manifold and an Einstein manifold, a warped product of ℝ and an Einstein manifold, and a singular warped product of ℝ² and a Ricci flat manifold. Compared with the previous four-dimensional study in, we have developed a novel method of {\it refined adapted frame fields} and overcome the main difficulty arising from a large number of Riemmannian connection components in dimension≥ 5. Next we have obtained a classification of {\it complete} gradient Ricci solitons with harmonic Weyl curvature. For the proof, using the real analytic nature of g and f, we elaborate geometric arguments to fit together local regions.Ricci solitonsEinstein metricsRicci-flat & Calabi–Yau4-manifoldsRotational symmetry & warped products