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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F22%3A50019286" target="_blank" >RIV/62690094:18470/22:50019286 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14310/22:00129117

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s13324-022-00701-w" target="_blank" >https://link.springer.com/article/10.1007/s13324-022-00701-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13324-022-00701-w" target="_blank" >10.1007/s13324-022-00701-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopické a homologické metody a nástroje úzce související s matematickou fyzikou</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Analysis and Mathematical Physics

ISSN

1664-2368

e-ISSN

1664-235X

Svazek periodika

12

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

52

Strana od-do

"Article Number: 93"

Kód UT WoS článku

000817297300001

EID výsledku v databázi Scopus

2-s2.0-85132967111