Year: 2026
Type: preprint
Abstract: We investigate the existence conditions for coupled extremal Kähler metrics on minimal ruled surfaces over a genus 2 Riemann surface. Using the Calabi ansatz to reduce the coupled extremal equations to ordinary differential equations, we prove that a pair of coupled extremal metrics exists for normalized Kähler classes $Ω_a$ and $Ω_b$ if and only if their parameters $(a, b)$ belong to an explicitly defined open region $\mathcal{S}_{\mathrm{ext}}$ in the positive real quadrant. Furthermore, we show that this existence region inherently contains the diagonal segment corresponding to classical extremal Kähler metrics.
Source: arXiv (Cornell University)
Author: Mete, Ramesh
Institution: Indian Institute of Technology Bombay
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213503672