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@article{2227338, author = {Chrysikos, Ioannis and Gregorovič, Jan and Winther, Henrik}, article_number = {6}, doi = {http://dx.doi.org/10.1007/s10231-022-01212-y}, keywords = {Quaternionic real form; Almost hypercomplex structures; Almost quaternionic structures; Almost hypercomplex skew-Hermitian structures; Almost quaternionic skewHermitian structures; Skew-Hermitian quaternionic forms; Scalar 2-forms; Intrinsic torsion}, language = {eng}, issn = {0373-3114}, journal = {Annali di Matematica Pura ed Applicata}, title = {Differential geometry of SO*(2n)-type structures}, url = {https://link.springer.com/article/10.1007/s10231-022-01212-y}, volume = {201}, year = {2022} }
TY - JOUR ID - 2227338 AU - Chrysikos, Ioannis - Gregorovič, Jan - Winther, Henrik PY - 2022 TI - Differential geometry of SO*(2n)-type structures JF - Annali di Matematica Pura ed Applicata VL - 201 IS - 6 SP - 2603-2662 EP - 2603-2662 PB - Springer SN - 03733114 KW - Quaternionic real form KW - Almost hypercomplex structures KW - Almost quaternionic structures KW - Almost hypercomplex skew-Hermitian structures KW - Almost quaternionic skewHermitian structures KW - Skew-Hermitian quaternionic forms KW - Scalar 2-forms KW - Intrinsic torsion UR - https://link.springer.com/article/10.1007/s10231-022-01212-y N2 - We study 4n-dimensional smooth manifolds admitting a SO∗(2 n) - or a SO∗(2 n) Sp(1) -structure, where SO∗(2 n) is the quaternionic real form of SO(2 n, C). We show that such G-structures, called almost hypercomplex/quaternionic skew-Hermitian structures, form the symplectic analogue of the better known almost hypercomplex/quaternionic-Hermitian structures (hH/qH for short). We present several equivalent definitions of SO∗(2 n) - and SO∗(2 n) Sp(1) -structures in terms of almost symplectic forms compatible with an almost hypercomplex/quaternionic structure, a quaternionic skew-Hermitian form, or a symmetric 4-tensor, the latter establishing the counterpart of the fundamental 4-form in almost hH/qH geometries. The intrinsic torsion of such structures is presented in terms of Salamon’s EH-formalism, and the algebraic types of the corresponding geometries are classified. We construct explicit adapted connections to our G-structures and specify certain normalization conditions, under which these connections become minimal. Finally, we present the classification of symmetric spaces K/L with K semisimple admitting an invariant torsion-free SO∗(2 n) Sp(1) -structure. This paper is the first in a series aiming at the description of the differential geometry of SO∗(2 n) - and SO∗(2 n) Sp(1) -structures. ER -
CHRYSIKOS, Ioannis, Jan GREGOROVIČ a Henrik WINTHER. Differential geometry of SO*(2n)-type structures. \textit{Annali di Matematica Pura ed Applicata}. Springer, 2022, roč.~201, č.~6, s.~2603-2662. ISSN~0373-3114. Dostupné z: https://dx.doi.org/10.1007/s10231-022-01212-y.
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