Geometric Analysis Talk
Speaker: Dr. Ramesh Mete, IIT Bombay
Host: Saikat Mazumdar
Title: On the existence of coupled extremal Kähler metrics on ruled surfaces.
Time, day and date: 3:00:00 PM – 4:00:00 PM, Wednesday, October 07
Venue: Ramanujan Hall
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 $\Omega_a$ and $\Omega_b$ if and only if their parameters $(a,b)$ belong to an explicitly defined open region $\mathcal{S}_{ext}$ in the positive real quadrant. Furthermore, we show that this existence region inherently contains the diagonal segment corresponding to classical extremal Kähler metrics.