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

CHRYSIKOS, Ioannis; Jan GREGOROVIČ a Henrik WINTHER. Differential geometry of SO*(2n)-type structures. Annali di Matematica Pura ed Applicata. Springer, 2022, roč. 201, č. 6, s. 2603-2662. ISSN 0373-3114. Dostupné z: https://doi.org/10.1007/s10231-022-01212-y.

Základní údaje

Originální název

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

Autoři

CHRYSIKOS, Ioannis; Jan GREGOROVIČ a Henrik WINTHER

Vydání

Annali di Matematica Pura ed Applicata, Springer, 2022, 0373-3114

---

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.000

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/22:00127021

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1007/s10231-022-01212-y

UT WoS

000855992300001

EID Scopus

2-s2.0-85138554325

Klíčová slova anglicky

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

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

---

Anotace

V originále

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.