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@article{2352377,
author = {Clemente, Gabriella Alexandrea},
article_number = {1},
keywords = {almost-complex structures; integrability; curvature},
language = {eng},
issn = {1331-0623},
journal = {Mathematical Communications},
title = {A curvature obstruction to integrability},
url = {https://www.mathos.unios.hr/mc/index.php/mc/article/view/4572/875},
volume = {28},
year = {2023}
}
TY - JOUR
ID - 2352377
AU - Clemente, Gabriella Alexandrea
PY - 2023
TI - A curvature obstruction to integrability
JF - Mathematical Communications
VL - 28
IS - 1
SP - 29-48
EP - 29-48
PB - University of Osijek
SN - 13310623
KW - almost-complex structures
KW - integrability
KW - curvature
UR - https://www.mathos.unios.hr/mc/index.php/mc/article/view/4572/875
N2 - 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.
ER -
CLEMENTE, Gabriella Alexandrea. A curvature obstruction to integrability. \textit{Mathematical Communications}. University of Osijek, 2023, vol.~28, No~1, p.~29-48. ISSN~1331-0623.
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