Algebraic Curvature Tensors of Einstein and Weakly Einstein Model Spaces

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.