Almost hypercomplex/quaternionic skew-Hermitian structures

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, C). Such G-structures form the symplectic analog of the well-known almost hypercomplex/quaternionic Hermitian structures, and we call them almost hypercomplex/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. Some examples and classification examples will be also discusssed. This talk is based on a joint work with J. Gregorovič (UHK) and H. Winther (Masaryk).

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.