A curvature obstruction to integrability

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F23%3A00134333" target="_blank" >RIV/00216224:14310/23:00134333 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mathos.unios.hr/mc/index.php/mc/article/view/4572/875" target="_blank" >https://www.mathos.unios.hr/mc/index.php/mc/article/view/4572/875</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A curvature obstruction to integrability

Popis výsledku v původním jazyce

The classical theory of G-structures, which include almost-complex structures, explains the relationship between the curvature of compatible connections and integrability. This note is an effort to understand how the curvature of Riemannian metrics can obstruct the integrability of almost-complex structures. It is shown that certain special complex structures cannot coexist with non-flat constant curvature metrics, and a formal variational realization of these structures is provided. The approach followed here is direct, meaning that it bypasses the classical theory. The idea is to find obstruction equations for the integrability of almost-complex structures by way of Nijenhuis tensor derivatives. These new equations involve the curvature of a torsion-free connection, and reveal the interplay between almost-complex and Riemannian geometries. Curvature scalars to detect non -complexity in the compact case then arise in a natural way.

Název v anglickém jazyce

A curvature obstruction to integrability

Popis výsledku anglicky

The classical theory of G-structures, which include almost-complex structures, explains the relationship between the curvature of compatible connections and integrability. This note is an effort to understand how the curvature of Riemannian metrics can obstruct the integrability of almost-complex structures. It is shown that certain special complex structures cannot coexist with non-flat constant curvature metrics, and a formal variational realization of these structures is provided. The approach followed here is direct, meaning that it bypasses the classical theory. The idea is to find obstruction equations for the integrability of almost-complex structures by way of Nijenhuis tensor derivatives. These new equations involve the curvature of a torsion-free connection, and reveal the interplay between almost-complex and Riemannian geometries. Curvature scalars to detect non -complexity in the compact case then arise in a natural way.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GC22-15012J" target="_blank" >GC22-15012J: Hladká a analytická regularita v CR geometrii</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Mathematical Communications

ISSN

1331-0623

e-ISSN

1848-8013

Svazek periodika

28

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

HR - Chorvatská republika

Počet stran výsledku

20

Strana od-do

29-48

Kód UT WoS článku

001012117800003

EID výsledku v databázi Scopus

2-s2.0-85147702711