2025/10/15 by Nguyen Gia Hien, Hien, Nguyen Gia, Michael Reiter +3
Mathematics · #32V05 #32V40 #53C30 #Advanced Algebra and Geometry #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2510.13252
openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
We classify CR maps from the hyperquadric of signature l>0 in ℂn, n≥ 3, to the local model for the tube over the null cone of a symmetric form in ℂn+1, up to CR automorphisms of the source and target. In contrast to the setting of the Heisenberg hypersurface in ℂ3 (i.e., the case l=0), studied earlier in Reiter--Son [27], our analysis uncovers two new equivalence classes of CR maps of geometric rank one and one new class of geometric rank two in the case n=3. In the case n≥ 4, we establish that all maps extend to local isometries of certain indefinite Kähler metrics. We further derive a classification of (local) proper holomorphic maps from the generalized unit ball \mathbbBnl into a generalized version of the Lie ball DIVm,l (the generalized classical domain of type~IV).