Solitons and affine projectively flat surfaces
Wlodzimierz Jelonek
TL;DR
This paper characterizes affine surfaces with projectively flat Blaschke structures, showing they are described by soliton equations when having constant Gauss affine curvature and indefinite metrics.
Contribution
It provides a local description of affine surfaces with projectively flat Blaschke structures using soliton equations, a novel connection in affine differential geometry.
Findings
Affine surfaces with projectively flat Blaschke structures are described by soliton equations.
Such surfaces with constant Gauss affine curvature have indefinite induced metrics.
The paper establishes a link between affine differential geometry and integrable systems.
Abstract
The aim of this paper is to give a local description of affine surfaces, whose induced Blaschke structure is projectively flat. We show that such affine surfaces with constant Gauss affine curvature and indefinite induced Blaschke metric are described by soliton equations.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology