https://neckpinch.com/authors/fabio-zuddas/New arXiv papers by Fabio Zuddas, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2510.06405arxiv:2510.06405Tue, 07 Oct 2025 00:00:00 GMTAndrea Loi, Roberto Mossa, Fabio ZUddas — We study the Bergman metric and introduce the Bergman dual on Cartan-Hartogs (CH) domains. For a bounded domain D in C^n with Bergman kernel K_D, we define the Bergman dual of (D, g_D) as (D*, g_D*), where D* is the maximal domain on which the modified kernel K_D*(z, zbar) = K_D(z, -zbar) is positive, and g_D* is the Kahler metric obtained from K_D*. For a Cartan-Hartogs domain M_Omega, mu we prove the equivalence of: (i) M_Omega, mu is biholomorphic to the unit ball; (ii) its Bergman metric is a Kahler-Ricci soliton; (iii) after rescaling by a constant factor, the Bergman dual is finitely projectively induced. Conditions (i) and (ii) are Bergman-metric analogues of classical rigidity for Kahler-Einstein metrics (related to Yau's problem and Cheng's conjecture) and to recent rigidity for Kahler-Ricci solitons. Condition (iii) emphasizes the duality viewpoint, inspired by bounded symmetric domains and their compact duals. We also compare our results with other canonical metrics on CH domains, namely g_Omega, mu and hat g_Omega, mu, and discuss open problems about the maximal domain on which the Bergman dual is defined.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryStability & uniquenessKähler–Einstein & K-stability https://arxiv.org/abs/2507.23606arxiv:2507.23606Thu, 31 Jul 2025 00:00:00 GMTAndrea Loi, Roberto Mossa, Fabio Zuddas — We prove a universal embedding theorem for flag manifolds: every flag manifold admits a holomorphic isometric embedding into an irreducible classical flag manifold. This result generalizes the classical celebrated embedding theorems of Takeuchi [30] and Nakagawa-Takagi [27]. Using this embedding, we establish new rigidity phenomena for holomorphic isometries between homogeneous Kähler manifolds. As a first immediate consequence we show the triviality of a Kähler-Ricci soliton submanifod of C × Ω, where C is a flag manifold and Ω is a homogeneous bounded domain. Secondly, we show that no weak-relative relationship can occur among the fundamental classes of homogeneous Kähler manifolds: flat spaces, flag manifolds, and homogeneous bounded domains. Two Kähler manifolds are said to be weak relatives if they share, up to local isometry, a common Kähler submanifold of complex dimension at least two. Our main result precisely shows that if E is (possibly indefinite) flat, C is a flag manifold, and Ω is a homogeneous bounded domain, then: E is not weak relative to C×Ω; C is not weak relative to E×Ω; Ω is not weak relative to E× C. This extends, in two independent directions, the rigidity theorem of Loi-Mossa [22]: we pass from relatives to the more flexible notion of weak relatives and dispense with the earlier "special" restriction on the flag-manifold factor. This result also unifies previous rigidity results from the literature, e.g., [5, 6, 7, 9, 12, 13, 32].Ricci solitonsKähler–Ricci solitonsKähler geometryHomogeneous spacesStability & uniqueness https://arxiv.org/abs/2109.15229arxiv:2109.15229Thu, 30 Sep 2021 00:00:00 GMTAndrea Loi, Filippo Salis, Fabio Zuddas — We prove that a radial Kaehler metric g is Kaehler-Einstein if and only if one of the following conditions is satisfied: 1. g is extremal and it is associated to a Kaehler-Ricci soliton; 2. two different generalized scalar curvatures of g are constant; 3. g is extremal (not cscK) and one of its generalized scalar curvature is constant.Ricci solitonsKähler–Ricci solitonsEinstein metricsKähler geometryScalar curvatureKähler–Einstein & K-stability