Almost complex structures on cotangent bundles and generalized geometry
type: Item
instance of: scholarly article
title: Almost complex structures on cotangent bundles and generalized geometry
zbMATH Open document ID: 1200.53031
author: Antonella Nannicini
published in: Journal of Geometry and Physics
publication date: 2010-09-24T00:00:00Z
review text: Let \(M\) be a smooth manifold with a torsion free connection \(\nabla\). The author studies a generalized complex structure of \(M\) as a complex structure on \(E = TM\oplus TM^{\star}\) and a class of such structures. The concept of \(\nabla\)-integrability was introduced for complex structures and here the integrability conditions are studied. In the case of the generalized complex structures introduced by \textit{N. Hitchin} [Q. J. Math. 54, No.~3, 281--308 (2003; Zbl 1076.32019)], the author compares the two concepts of integrability. The conditions under which they coincide are investigated.
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 5791214
zbMATH Keywords: generalized geometry
zbMATH Keywords: symplectic vector bundles
zbMATH Keywords: calibrated complex structures
MaRDI profile type: Publication
full work available at URL: j.geomphys.2010.06.004
OpenAlex ID: W1994594961
cites work: Q4400895
cites work: Generalized Calabi-Yau Manifolds
cites work: Generalized complex geometry
cites work: Q3134937
cites work: The tangent bundle of an almost complex manifold
cites work: Calibrated complex structures on the generalized tangent bundle of a Riemannian manifold
DOI: 10.1016/J.GEOMPHYS.2010.06.004
description: scientific article; zbMATH DE number 5791214