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Decomposable Model Spaces And A Topological Approach To Curvature, Kevin M. Tully
Decomposable Model Spaces And A Topological Approach To Curvature, Kevin M. Tully
Rose-Hulman Undergraduate Mathematics Journal
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 …