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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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