Cohomological expression of the curvature of K\"ahler moduli
Gunnar {\TH}\'or Magn\'usson
TL;DR
This paper provides a cohomological framework to express the Levi-Civita connection and curvature tensor of the Kähler cone's natural Riemannian metric, also analyzing conditions for its completeness.
Contribution
It introduces cohomological formulas for the Levi-Civita connection and curvature tensor of the Kähler cone metric, advancing understanding of its geometric properties.
Findings
Cohomological expressions for Levi-Civita connection
Formulas for the curvature tensor of the Kähler cone
Conditions for metric completeness
Abstract
The K\"ahler cone of a compact K\"ahler manifold carries a natural Riemannian metric, given by the intersection product of its cohomology ring. We give cohomological expressions for the Levi-Civita connection and curvature tensor of this metric, and determine when the metric is complete.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research