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Keywords:
curvature model; curvature homogeneous; homothethy curvature homogeneous
curvature model; curvature homogeneous; homothethy curvature homogeneous
Summary:
We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders, and demonstrate that for certain model spaces and realizations, homothety curvature homogeneity implies curvature homogeneity.
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