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Constructing Spanning Sets Of Affine Algebraic Curvature Tensors, Stephen J. Kelly
Constructing Spanning Sets Of Affine Algebraic Curvature Tensors, Stephen J. Kelly
Rose-Hulman Undergraduate Mathematics Journal
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.