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EnglishIn the present article we carry on a systematic study of 3-quasi-Sasakianmanifolds. 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 showthat 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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| Titolo: | 3-quasi-Sasakian manifolds |
| Autori: | |
| Data di pubblicazione: | 2008 |
| Rivista: | |
| Abstract: | In the present article we carry on a systematic study of 3-quasi-Sasakianmanifolds. 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 showthat 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. |
| Handle: | http://hdl.handle.net/11584/20014 |
| Tipologia: | 1.1 Articolo in rivista |
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