A class of new complete affine maximal type hypersurfaces
Yalin Sun, Ruiwei Xu
TL;DR
This paper classifies special Calabi hypersurfaces with negative constant sectional curvature and introduces new complete affine hypersurfaces satisfying affine maximal and Abreu equations with negative scalar curvature.
Contribution
It provides a classification of certain Calabi hypersurfaces and constructs new complete affine hypersurfaces satisfying key geometric equations.
Findings
Classification of special Calabi hypersurfaces with negative curvature
Construction of new complete affine hypersurfaces satisfying affine maximal and Abreu equations
Identification of hypersurfaces with negative constant scalar curvature
Abstract
In this paper we classify a kind of special Calabi hypersurfaces with negative constant sectional curvature in Calabi affine geometry. Meanwhile, we find a class of new Euclidean complete and Calabi complete affine hypersurfaces, which satisfy the affine maximal type equation and the Abreu equation with negative constant scalar curvatures.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Holomorphic and Operator Theory · Algebraic Geometry and Number Theory