Detailed Information on Publication Record
2023
A curvature obstruction to integrability
CLEMENTE, Gabriella AlexandreaBasic information
Original name
A curvature obstruction to integrability
Authors
CLEMENTE, Gabriella Alexandrea (840 United States of America, guarantor, belonging to the institution)
Edition
Mathematical Communications, University of Osijek, 2023, 1331-0623
Other information
Language
English
Type of outcome
Článek v odborném periodiku
Field of Study
10101 Pure mathematics
Country of publisher
Croatia
Confidentiality degree
není předmětem státního či obchodního tajemství
References:
Impact factor
Impact factor: 0.400 in 2022
RIV identification code
RIV/00216224:14310/23:00134333
Organization unit
Faculty of Science
UT WoS
001012117800003
Keywords in English
almost-complex structures; integrability; curvature
Tags
Tags
International impact, Reviewed
Změněno: 21/12/2023 10:55, Mgr. Marie Šípková, DiS.
Abstract
V originále
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.
Links
| GC22-15012J, research and development project |
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