TY - JOUR AU - Kaitlin Ragosta PY - 2020/02/19 Y2 - 2024/03/28 TI - Canonical Expressions of Algebraic Curvature Tensors JF - The PUMP Journal of Undergraduate Research JA - PUMP J. Undergrad. Res. VL - 3 IS - 0 SE - Articles DO - 10.46787/pump.v3i0.2253 UR - https://journals.calstate.edu/pump/article/view/2253 AB - Algebraic curvature tensors can be expressed in a variety of ways, and it is helpful to develop invariants that can distinguish between them. One potential invariant is the signature of R, which could be defined in a number of ways, similar to the signature of an inner product. This paper shows that any algebraic curvature tensor defined on a vector space V with dim(V) = n can be expressed using only canonical algebraic curvature tensors from forms with rank k or higher for any k in {2,...,n}, and that such an expression is not unique, eliminating some possibilities for what one might define the signature of R to be. We also provide bounds on the minimum number of algebraic curvature tensors of rank k needed to express any given R. ER -