Další formáty:
BibTeX
LaTeX
RIS
@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, roč.~28, č.~1, s.~29-48. ISSN~1331-0623.
|