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Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

Mathematics

Rose-Hulman Institute of Technology

Journal

2023

Differential geometry

Articles 1 - 1 of 1

Full-Text Articles in Physical Sciences and Mathematics

Constructing Spanning Sets Of Affine Algebraic Curvature Tensors, Stephen J. Kelly May 2023

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.