3-quasi-Sasakian manifolds

Details 3-quasi-Sasakian manifolds 3-quasi-Sasakian manifolds

2007-06-11

arxiv.org/abs/0706.1438v5

Ann. Glob. Anal. Geom. 33 (2008), 397-409.

Mathematics

Differential Geometry

17 pages, minor modifications, references updated

Scientific paper

10.1007/s10455-007-9093-5

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.

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