$G_2$-instantons on nilpotent Lie groups

Abstract: In this talk we will discuss recent advancements on G$_2$-instantons on 7-dimensional 2-step nilpotent Lie groups endowed with a left-invariant coclosed G$_2$-structures. I will present necessary and sufficient conditions for the characteristic connection of the G$_2$-structure to be an instanton, in terms of the torsion of the G$_2$-structure, the torsion of the connection and the Lie group structure. These conditions allow to show that the metrics corresponding to the G$_2$-instantons define a naturally reductive structure on the simply connected 2-step nilpotent Lie group with left-invariant Riemannian metric. This is a joint work with Andrew Clarke and Andrés Moreno.

differential geometry

Audience: researchers in the topic

( paper )

---

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.

---