We discuss 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 hypercomplex/quaternionic Hermitian structures, and hence we cal them hypercomplex / quaternionic skew-Hermitian structures, respectively. We will describe the basic data encoding such geometric structures, their intrinsic torsion, related 1st-order integrability conditions and some classification examples, if time permitted. This talk is based on joint works with J. Gregorovič (UHK) and H. Winther (Masaryk)

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We open ZOOM at 13.15 for virtual coffee and close at 15... more

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We open ZOOM at 13.15 for virtual coffee and close at 15... more