A curvature obstruction to integrability
The result's identifiers
Result code in 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>
Result on the web
<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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Alternative languages
Result language
angličtina
Original language name
A curvature obstruction to integrability
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GC22-15012J" target="_blank" >GC22-15012J: Smooth and analytic regularity in CR geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Communications
ISSN
1331-0623
e-ISSN
1848-8013
Volume of the periodical
28
Issue of the periodical within the volume
1
Country of publishing house
HR - CROATIA
Number of pages
20
Pages from-to
29-48
UT code for WoS article
001012117800003
EID of the result in the Scopus database
2-s2.0-85147702711