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Algebraic restrictions on geometric realizations of curvature models. (English) Zbl 07396182

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.

MSC:

53B30 Local differential geometry of Lorentz metrics, indefinite metrics
15A69 Multilinear algebra, tensor calculus
53B15 Other connections
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