Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 033, 25 pages      arXiv:2009.00670      https://doi.org/10.3842/SIGMA.2021.033

Invariants of Surfaces in Three-Dimensional Affine Geometry

Örn Arnaldsson a and Francis Valiquette b
a) Department of Mathematics, University of Iceland, Reykjavik, Ssn. 600169-2039, Iceland
b) Department of Mathematics, Monmouth University, West Long Branch, NJ 07764, USA

Received September 03, 2020, in final form March 21, 2021; Published online March 30, 2021

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.

Key words: affine group; differential invariants; moving frames.

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