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@article{1875461,
author = {Chrysikos, Ioannis and Gregorovič, Jan and Winther, Henrik},
article_number = {4},
doi = {http://dx.doi.org/10.1007/s13324-022-00701-w},
keywords = {Almost hypercomplex/quaternionic structures; Almost hypercomplex/quaternionic skew-Hermitian structures; Adapted connections; Torsion types; Integrability conditions; Bundle of Weyl structures},
language = {eng},
issn = {1664-2368},
journal = {Analysis and Mathematical Physics},
title = {Differential geometry of SO*(2n)-type structures-integrability},
url = {https://link.springer.com/article/10.1007/s13324-022-00701-w},
volume = {12},
year = {2022}
}
TY - JOUR
ID - 1875461
AU - Chrysikos, Ioannis - Gregorovič, Jan - Winther, Henrik
PY - 2022
TI - Differential geometry of SO*(2n)-type structures-integrability
JF - Analysis and Mathematical Physics
VL - 12
IS - 4
SP - 1-52
EP - 1-52
PB - Springer
SN - 16642368
KW - Almost hypercomplex/quaternionic structures
KW - Almost hypercomplex/quaternionic skew-Hermitian structures
KW - Adapted connections
KW - Torsion types
KW - Integrability conditions
KW - Bundle of Weyl structures
UR - https://link.springer.com/article/10.1007/s13324-022-00701-w
N2 - We study almost hypercomplex skew-Hermitian structures and almost quaternionic skew-Hermitian structures, as the geometric structures underlying SO*(2n)- and SO*(2n)Sp(1)-structures, respectively. The corresponding intrinsic torsions were computed in the previous article in this series, and the algebraic types of the geometries were derived, together with the minimal adapted connections (with respect to certain normalizations conditions). Here we use these results to present the related first-order integrability conditions in terms of the algebraic types and other constructions. In particular, we use distinguished connections to provide a more geometric interpretation of the presented integrability conditions and highlight some features of certain classes. The second main contribution of this note is the illustration of several specific types of such geometries via a variety of examples. We use the bundle of Weyl structures and describe examples of SO*(2n)Sp(1)-structures in terms of functorial constructions in the context of parabolic geometries.
ER -
CHRYSIKOS, Ioannis, Jan GREGOROVIČ a Henrik WINTHER. Differential geometry of SO*(2n)-type structures-integrability. \textit{Analysis and Mathematical Physics}. Springer, 2022, roč.~12, č.~4, s.~1-52. ISSN~1664-2368. Dostupné z: https://dx.doi.org/10.1007/s13324-022-00701-w.
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