30 nov 2021 -- 14:30

DIMaI, Firenze (online)

Seminario di Geometria Differenziale e Analisi Complessa del Dipartimento di Matematica e Informatica "Ulisse Dini" dell'Università di Firenze

**Abstract.**

This talk provides a short introduction to the differential geometry of $4n$-dimensional manifolds admitting a $SO^{*}(2n)$-structure, or a $SO^{*}(2n)Sp(1)$-structure, where $SO^{*}(2n)$ denotes the quaternionic real form of $SO(2n, \mathbb{C})$. Such $G$-structures can be viewed as the symplectic analog of the well-known almost hypercomplex Hermitian and almost quaternionic Hermitian structures. Thus it is reasonable to call them almost hypercomplex skew-Hermitian and almost quaternionic skew-Hermitian structures, respectively. We describe the basic data encoding such geometric structures, and then we focus on their intrinsic torsion and related 1st-order integrability conditions. This talk is based on joint works with J. Gregorovič (UHK) and H. Winther (Masaryk).