Algebraic Curvature Tensors of Einstein and Weakly Einstein Model Spaces

Authors

  • Roberta Shapiro Rutgers University

DOI:

https://doi.org/10.46787/pump.v2i0.170

Keywords:

canonical algebraic curvature tensor, Einstein space, weakly Einstein

Abstract

This research investigates the restrictions on the symmetric bilinear form with associated algebraic curvature tensor R in Einstein and Weakly Einstein model spaces. We show that if a model space is Einstein and has a positive definite inner product, then: if the scalar curvature is non-negative, the model space has constant sectional curvature, and if the scalar curvature is negative, the matrix associated to the symmetric bilinear form can have at most two eigenvalues.

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Published

2019-03-01

How to Cite

Shapiro, R. (2019). Algebraic Curvature Tensors of Einstein and Weakly Einstein Model Spaces. The PUMP Journal of Undergraduate Research, 2, 30–43. https://doi.org/10.46787/pump.v2i0.170