CR-twistor spaces over manifolds with G2 - and Spin(7)-structures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00572817" target="_blank" >RIV/67985840:_____/23:00572817 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10231-023-01307-0" target="_blank" >https://doi.org/10.1007/s10231-023-01307-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10231-023-01307-0" target="_blank" >10.1007/s10231-023-01307-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

CR-twistor spaces over manifolds with G2 - and Spin(7)-structures

Popis výsledku v původním jazyce

In 1984 LeBrun constructed a CR-twistor space over an arbitrary conformal Riemannian 3-manifold and proved that the CR-structure is formally integrable. This twistor construction has been generalized by Rossi in 1985 for m-dimensional Riemannian manifolds endowed with a (m- 1) -fold vector cross product (VCP). In 2011 Verbitsky generalized LeBrun’s construction of twistor-spaces to 7-manifolds endowed with a G 2-structure. In this paper we unify and generalize LeBrun’s, Rossi’s and Verbitsky’s construction of a CR-twistor space to the case where a Riemannian manifold (M, g) has a VCP structure. We show that the formal integrability of the CR-structure is expressed in terms of a torsion tensor on the twistor space, which is a Grassmannian bundle over (M, g). If the VCP structure on (M, g) is generated by a G 2- or Spin (7) -structure, then the vertical component of the torsion tensor vanishes if and only if (M, g) has constant curvature, and the horizontal component vanishes if and only if (M, g) is a torsion-free G 2 or Spin (7) -manifold. Finally we discuss some open problems.

Název v anglickém jazyce

CR-twistor spaces over manifolds with G2 - and Spin(7)-structures

Popis výsledku anglicky

In 1984 LeBrun constructed a CR-twistor space over an arbitrary conformal Riemannian 3-manifold and proved that the CR-structure is formally integrable. This twistor construction has been generalized by Rossi in 1985 for m-dimensional Riemannian manifolds endowed with a (m- 1) -fold vector cross product (VCP). In 2011 Verbitsky generalized LeBrun’s construction of twistor-spaces to 7-manifolds endowed with a G 2-structure. In this paper we unify and generalize LeBrun’s, Rossi’s and Verbitsky’s construction of a CR-twistor space to the case where a Riemannian manifold (M, g) has a VCP structure. We show that the formal integrability of the CR-structure is expressed in terms of a torsion tensor on the twistor space, which is a Grassmannian bundle over (M, g). If the VCP structure on (M, g) is generated by a G 2- or Spin (7) -structure, then the vertical component of the torsion tensor vanishes if and only if (M, g) has constant curvature, and the horizontal component vanishes if and only if (M, g) is a torsion-free G 2 or Spin (7) -manifold. Finally we discuss some open problems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

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

202

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

23

Strana od-do

1931-1953

Kód UT WoS článku

000934589900001

EID výsledku v databázi Scopus

2-s2.0-85147737670