Remarks on the quadratic orthogonal bisectional curvature. (English) Zbl 1496.32034
Summary: We exhibit a curious link between the Quadratic Orthogonal Bisectional Curvature, combinatorics, and distance geometry. The Weitzenböck 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.
MSC:
| 32Q10 | Positive curvature complex manifolds |
| 32Q15 | Kähler manifolds |
| 05C22 | Signed and weighted graphs |
Keywords:
quadratic orthogonal bisectional curvature; real bisectional curvature; Kähler C-spaces; generalized Hartshorne conjecture; Euclidean distance matricesReferences:
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