Invariants of Surfaces in Three-Dimensional Affine Geometry
\"Orn Arnaldsson, Francis Valiquette
TL;DR
This paper investigates the differential invariants of surfaces in three-dimensional affine geometry using moving frames, revealing that for various point types, the invariant algebra is typically generated by a single invariant.
Contribution
It introduces a method to analyze the algebra of differential invariants for surfaces in affine geometry, showing generically it is generated by one invariant for different point types.
Findings
The algebra of differential invariants is non-trivial for elliptic, hyperbolic, and parabolic points.
In most cases, the algebra is generated by a single invariant.
The method of moving frames effectively analyzes these invariants.
Abstract
Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is non-trivial, then it is generically generated by a single invariant.
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