Canonical Expressions of Algebraic Curvature Tensors

Authors

  • Kaitlin Ragosta Boston University

DOI:

https://doi.org/10.46787/pump.v3i0.2253

Keywords:

canonical algebraic curvature tensor; signature conjecture; linear independence

Abstract

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.

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Published

2020-02-19

How to Cite

Ragosta, K. (2020). Canonical Expressions of Algebraic Curvature Tensors. The PUMP Journal of Undergraduate Research, 3, 52–61. https://doi.org/10.46787/pump.v3i0.2253