3-quasi-Sasakian manifolds
Differential Geometry
2008-04-29 v5
Abstract
In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the orthogonal group or an abelian one. We show that 3-quasi-Sasakian manifolds have a well-defined rank, obtaining a rank-based classification. Furthermore, we prove a splitting theorem for these manifolds assuming the integrability of one of the almost product structures. Finally, we show that the vertical distribution is a minimum of the corrected energy.
Keywords
Cite
@article{arxiv.0706.1438,
title = {3-quasi-Sasakian manifolds},
author = {Beniamino Cappelletti Montano and Antonio De Nicola and Giulia Dileo},
journal= {arXiv preprint arXiv:0706.1438},
year = {2008}
}