Remarks on the Quadratic Orthogonal Bisectional Curvature

Abstract

We exhibit a curious link between the Quadratic Orthogonal Bisectional Curvature, combinatorics, and distance geometry. The Weitzenb\"ock curvature operator, acting on real (1,1)--forms, is realized as the Dirichlet energy of a finite graph, weighted by a matrix of the curvature. These results also illuminate the difference in the nature of the Quadratic Orthogonal Bisectional Curvature and the Real Bisectional Curvature.