Differential geometry of SO*(2n)-type structures

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019715" target="_blank" >RIV/62690094:18470/22:50019715 - isvavai.cz</a>
Alternative codes found
RIV/00216224:14310/22:00127021
Result on the web
<a href="https://link.springer.com/article/10.1007/s10231-022-01212-y" target="_blank" >https://link.springer.com/article/10.1007/s10231-022-01212-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10231-022-01212-y" target="_blank" >10.1007/s10231-022-01212-y</a>

Result language
angličtina
Original language name
Differential geometry of SO*(2n)-type structures
Original language description
We study 4n-dimensional smooth manifolds admitting a SO*(2n)- or a SO*(2n) Sp (1)-structure, where SO*(2n) is the quaternionic real form of SO(2n, 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*(2n)-and SO*(2n) 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 KIL with K semisimple admitting an invariant torsion-free SO*(2n) Sp (1)-structure. This paper is the first in a series aiming at the description of the differential geometry of SO*(2n)- and SO*(2n) Sp (1)-structures.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ19-14466Y" target="_blank" >GJ19-14466Y: Special metrics in supergravity and new G-structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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