This research investigates a model space invariant known as k-plane constant vector curvature, traditionally studied when k=2, and introduces a new invariant, (m,k)-plane constant vector curvature. We prove that the sets of k-plane and (m,k)-plane constant vector curvature values are connected, compact subsets of the real numbers and establish several relationships between the curvature values of a decomposable model space and its component spaces. We also prove that every decomposable model space with a positive-definite inner product has k-plane constant vector curvature for some integer k>1. In two examples, we provide the first instance of a model space with (m,k)-plane constant vector curvature and leverage our theorems to efficiently calculate the k-plane constant vector curvature values of a decomposable model space. This research further characterizes model spaces by assigning new basis-independent values to its various subspaces and allows us to easily construct model spaces with prescribed curvature values.
Tully, Kevin M.
"Decomposable Model Spaces and a Topological Approach to Curvature,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 22:
2, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol22/iss2/8