A curvature formula for the complexified index cone of a cubic form
Thomas Trenner
TL;DR
This paper derives a curvature formula for a Kaehler metric associated with a cubic form on its complexified index cone, linking it to mirror symmetry and the Weil-Petersson metric.
Contribution
It provides a rigorous proof of the curvature formula for the Kaehler metric derived from a cubic form, connecting it to mirror symmetry principles.
Findings
Curvature formula for the Kaehler metric is established.
The metric asymptotically matches the Weil-Petersson metric under mirror symmetry.
The work utilizes the theory of special Kaehler manifolds.
Abstract
We study the Kaehler metric given by the logarithm of a cubic form on its complexified index cone. Under mirror symmetry, this metric should asymptotically correspond to the Weil-Petersson metric. Using the theory of special Kaehler manifolds, a proof of a curvature formula for this metric is given.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research