Dept Math & Stat UiT, Forskningsparken B459
  1 Nov 2021 Mon 13:00-14:00

Ioannis Chrysikos (University Hradec Kralové)

Hypercomplex/quaternionic skew-Hermitian structures

We present a short introduction to differential geometry of 4n-dimensional manifolds admitting SO*(2n)- or SO*(2n)Sp(1)-structure, where SO*(2n) denotes the quaternionic real form of SO(2n,C). Such G-structures form the symplectic analog of the well-known hypercomplex/quaternionic Hermitian structures, which we call hypercomplex/quaternionic skew-Hermitian structures, respectively.

The basic data encoding such geometric structures will be described, their intrinsic torsion, as well related 1st-order integrability conditions and some classification examples. This talk is based on a joint work with J. Gregorovic (UHK) and H. Winther (Masaryk).