A Property of Geodesics in Special K\"ahler Geometry
Sergio Cecotti
TL;DR
This paper investigates the properties of stable geodesics in the special K"ahler geometry associated with 4d $\
Contribution
It provides an explicit description of stable geodesics in QFT special K"ahler geometry and shows that no closed stable geodesics exist.
Findings
Complete stable geodesics are highly restricted.
No closed stable geodesic exists in this geometry.
The Myers method is applicable to related geometric problems.
Abstract
We study the stable geodesics of the QFT special K\"ahler geometry ( Seiberg-Witten geometry of 4d QFT) using the Myers argument. Complete stable geodesics are quite restricted, and can be described very explicitly. In particular no closed stable geodesic exists. We comment on the application of the Myers method to related problems, including geodesics in moduli spaces of Calabi-Yau 3-folds.
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Taxonomy
TopicsGeometry and complex manifolds · Algebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows