Classification of Calabi Hypersurfaces with parallel Fubini-Pick form
Ruiwei Xu, Miaoxin Lei
TL;DR
This paper classifies 2- and 3-dimensional Calabi hypersurfaces that have a parallel Fubini-Pick form, advancing understanding of their geometric structure.
Contribution
It provides a complete classification of Calabi hypersurfaces with parallel Fubini-Pick form in low dimensions, a new result in affine differential geometry.
Findings
Complete classification of 2-dimensional Calabi hypersurfaces
Complete classification of 3-dimensional Calabi hypersurfaces
Identification of geometric properties related to parallel Fubini-Pick form
Abstract
In this paper, we present the classification of 2 and 3-dimensional Calabi hypersurfaces with parallel Fubini-Pick form with respect to the Levi-Civita connection of the Calabi metric.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology