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We extend the definition of curvature homogeneity of type (1,3) to includethe possibility that there is a homothety between any two points of a manifoldpreserving the first r covariant derivatives of the curvature operatorsimultaneously; we call this strong curvature homogeneity of type (1,3) up toorder r. We characterize these properties in terms of model spaces. Inaddition, we also present two families of three-dimensional Lorentzian metricson Euclidean space to exhibit the behavior of this property. The first exampleis curvature homogeneous of type (1,3) of all orders, but is not locallyhomogeneous. Within this first family, being strongly curvature homogeneous oftype (1,3) up to order 1 implies local homogeneity. The second example isstrongly curvature homogeneous of type (1,3) up to order one, and is notlocally homogeneous, showing that this new definition is not a trivial one.Within this family, being strongly curvature homogeneous of type (1,3) up toorder 2 implies local homogeneity.

Singer invariants and strongly curvature homogeneous manifolds of type (1,3)