TY - JOUR
AU - Kaitlin Ragosta
PY - 2020/02/19
Y2 - 2022/10/03
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 -
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 -