Generalized complex structures on nilmanifolds
type: Item
instance of: scholarly article
title: Generalized complex structures on nilmanifolds
zbMATH Open document ID: 1079.53106
author: Gil R. Cavalcanti
author: Marco Gualtieri
published in: The Journal of Symplectic Geometry
publication date: 2005-08-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0404451
review text: This paper concerns classification of nilmanifolds \(M\) endowed with a so-called generalized complex strucure, (Hitchin), i.e., an almost complex structure \({\mathcal J}\) on the vector bundle \(\pi:E\equiv TM\oplus T^*M\to M\), such that it satisfies some further requirements: (i) \({\mathcal J}\) is orthogonal with respect to the natural inner product on sections of \(E\to M\); (ii) the \(+i\)-eigenbundle of \({\mathcal J}\) is required to be involutive with respect to the Courant bracket. In particular the authors specialize their investigation on \(6\)-dimensional nilmanifolds, where there exist some types without standard complex or symplectic structure. The results presented in this paper are obtained with standard techniques of almost complex bundles geometry.
reviewed by: Agostino Prástaro
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 2199035
zbMATH Keywords: nilmanifolds
zbMATH Keywords: generalized complex structures
MaRDI profile type: Publication
arXiv ID: math/0404451
DOI: 10.4310/JSG.2004.V2.N3.A5
description: scientific article