Algebraic Curvature Tensors of Einstein and Weakly Einstein Model Spaces

  • Roberta Shapiro Rutgers University
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.

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. Retrieved from https://journals.calstate.edu/pump/article/view/170