https://neckpinch.com/authors/giovanni-placini/New arXiv papers by Giovanni Placini, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2307.11500/arxiv:2307.11500Fri, 21 Jul 2023 00:00:00 GMTAndrea Loi, Giovanni Placini — We introduce a large class of canonical Kähler metrics, called in this paper well-behaved, extending metrics induced by complex space forms. We study Kähler–Ricci iterations of well-behaved metrics on compact and non-compact Kähler manifolds. That is, we are interested in well-behaved metrics for which the iteration of the Ricci operator is a multiple of a Kähler metric, i.e., ρ_ω^k=λΩ. In particular, when k=1, under some condition on the maximal domain of definition of canonical coordinates, we show that λ is forced to be positive. Moreover, for arbitrary k, we prove two additional results. Namely, if ω and Ω are induced by a flat metric, then ω is Ricci-flat. Finally, if a Kähler-Ricci soliton Ω arises as Kähler–Ricci iteration of a metric ω induced by a complex space form, then the Kähler–Ricci soliton is forced to be trivial, that is, Kähler–Einstein. These three theorems extend well known results on Kähler–Einstein metrics to higher iterations of the Ricci operator and a larger class of metrics.Ricci solitonsKähler–Ricci solitonsEinstein metricsRicci-flat & Calabi–YauSphere theoremsKähler geometryBoundaries & non-compactKähler–Einstein & K-stability https://neckpinch.com/papers/2306.17783/arxiv:2306.17783Fri, 30 Jun 2023 00:00:00 GMTRoberto Mossa, Giovanni Placini — We discuss local Sasakian immersion of Sasaki-Ricci solitons (SRS) into fiber products of homogeneous Sasakian manifolds. In particular, we prove that SRS locally induced by a large class of fiber products of homogeneous Sasakian manifolds are, in fact, η-Einstein. The results are stronger for immersions into Sasakian space forms. Moreover, we show an example of a Kähler-Ricci soliton on ℂⁿ which admits no local holomorphic isometry into products of homogeneous bounded domains with flat Kähler manifolds and generalized flag manifolds.Ricci solitonsKähler–Ricci solitonsSphere theoremsKähler geometryHomogeneous spacesSasakian & contact geometry