Algebraic restrictions on geometric realizations of curvature models

Dunn, Corey   ; Smith, Zoë

Archivum mathematicum, Tome 57 (2021) no. 3, pp. 175-194

Abstract (VO)

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.

Détail

DOI : 10.5817/AM2021-3-175

Classification : 15A69, 53B15, 53B30
Keywords: curvature model; curvature homogeneous; homothethy curvature homogeneous

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