In this paper, we construct two spanning sets for the affine algebraic curvature tensors. We then prove that every 2-dimensional affine algebraic curvature tensor can be represented by a single element from either of the two spanning sets. This paper provides a means to study affine algebraic curvature tensors in a geometric and algebraic manner similar to previous studies of canonical algebraic curvature tensors.

Author Bio

This research was done at the California State University, San Bernardino REU by Steve Kelly. When not researching math, Steve enjoys curling, reading, and swimming.