On a surface isolated by Gambier
Runliang Lin (Tsinghua, Beijing), Robert Conte (ENS Cachan, CNRS, U, Paris-Saclay)
TL;DR
This paper establishes a Lax pair for Voss and Guichard surfaces and characterizes Gambier's surfaces using a third Painlevé function, linking geometric surface theory with integrable systems.
Contribution
It introduces a Lax pair for specific surfaces and connects Gambier's surfaces to a third Painlevé function, advancing the understanding of their integrable structure.
Findings
Lax pair formulated for Voss and Guichard surfaces
Gambier's surfaces characterized by a third Painlevé function
Bridges surface geometry with integrable systems theory
Abstract
We provide a Lax pair for the surfaces of Voss and Guichard, and we show that such particular surfaces considered by Gambier are characterized by a third Painlev\'e function.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology