Hermitian curvature flow and HKT geometry

Abstract: We introduce a Hermitian curvature flow that preserves HKT geometry and whose fixed points are HKT–Einstein metrics. This flow is strictly related to the quaternionic Monge–Ampère equation. We develop a basic regularity theory and establish a monotonicity formula for the Chern scalar curvature. We then formulate a conjecture characterizing the maximal existence time and prove a conditional version of it; in real dimension four, we establish the conjecture unconditionally. Finally, we construct a divergent sequence of HKT–Einstein metrics on quaternionic Hopf surfaces. These provide the first non-homogeneous examples of HKT–Einstein metrics in the literature and highlight the subtlety of the long-time convergence problem. This is a joint paper with J. Streets.

differential geometry

Audience: researchers in the topic

Geometry Webinar AmSur /AmSul

Series comments: The Geometry Webinar AmSur/AmSul is promoted by differential geometry groups from Universities in Argentina and Brazil. The webinar happens weekly on Fridays at 14h00 (GMT-3) via Google Meet. Talks will be in Spanish, Portuguese or English. This virtual seminar aims to establish the contact with several research groups and mathematicians from Latin America. Everybody is invited to participate writing to the contact e-mail: geodif@unicamp.br

For each talk, the Google Meet link will be sent.