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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216224:14310/22:00127021

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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&apos;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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-14466Y" target="_blank" >GJ19-14466Y: Speciální metriky v supergravitaci a nové G-struktury</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annali di Matematica Pura ed Applicata

ISSN

0373-3114

e-ISSN

1618-1891

Svazek periodika

201

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

60

Strana od-do

2603-2662

Kód UT WoS článku

000855992300001

EID výsledku v databázi Scopus

2-s2.0-85138554325