2021/11/24 by Miaoxin Lei, Ruiwei Xu, Lei, Miaoxin +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2112.01947
openalex publication_date 2021/11/24 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
The classifications of locally strongly convex equiaffine hypersurfaces (resp. centroaffine hypersurfaces) with parallel Fubini-Pick form with respect to the Levi-Civita connection of the Blaschke-Berwald affine metric (resp. centroaffine metric) have been completed by several geometers in the last decades, see \citeHLV and \citeCHM. In this paper we define a generalized Calabi product in Calabi geometry and prove decomposition theorems in terms of their Calabi invariants. As the main result, we obtain a complete classification of Calabi hypersurfaces in \bbrn+1 with parallel Fubini-Pick form with respect to the Levi-Civita connection of the Calabi metric. This result is a counterpart in Calabi geometry of the classification theorems in equiaffine situation \citeHLV and centroaffine situation \citeCHM.