Algebraic restrictions on geometric realizations of curvature models

Corey Dunn and Zoë Smith

Address:
Mathematics Department, California State University at San Bernardino, San Bernardino, CA 92407, USA
Mathematics Department, University of Chicago, Chicago, IL 60637, USA

E-mail:
cmdunn@csusb.edu
smithzj@uchicago.edu

Abstract: 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.

AMSclassification: primary 53B30; secondary 15A69, 53B15.

Keywords: curvature model, curvature homogeneous, homothethy curvature homogeneous.

DOI: 10.5817/AM2021-3-175