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EnglishWe extend to the semi-Riemannian context the well-known results obtained by Blair, Ludden and Yano on toroidal principal bundles endowed with a metric globally framed f-structure. In this way we obtain examples of compact indefinite S-manifolds. Then, we define an indefinite S-structure on the Lie group U(2) with a Lorentz left-invariant metric and, applying our results, we construct commutative diagrams involving semi-Riemannian submersions and Hopf fibrations. We also prove that U(2) with such a structure is foliated by Reinhart lightlike hypersurfaces. Finally, we consider a normal indefinite globally framed f-structure on the Lie group U(4) pro- ving that it projects on U(4)/U(3) in a Sasakian structure isomorphic to the standard Sasakian structure of S^7
Examples of indefinite globally framed f-structures on compact Lie groups / BRUNETTI L; PASTORE A.M.. - In: PUBLICATIONES MATHEMATICAE. - ISSN 0033-3883. - 80:1-2(2012), pp. 215-234.
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| Titolo: | Examples of indefinite globally framed f-structures on compact Lie groups |
| Autori: | |
| Data di pubblicazione: | 2012 |
| Rivista: | |
| Citazione: | Examples of indefinite globally framed f-structures on compact Lie groups / BRUNETTI L; PASTORE A.M.. - In: PUBLICATIONES MATHEMATICAE. - ISSN 0033-3883. - 80:1-2(2012), pp. 215-234. |
| Abstract: | We extend to the semi-Riemannian context the well-known results obtained by Blair, Ludden and Yano on toroidal principal bundles endowed with a metric globally framed f-structure. In this way we obtain examples of compact indefinite S-manifolds. Then, we define an indefinite S-structure on the Lie group U(2) with a Lorentz left-invariant metric and, applying our results, we construct commutative diagrams involving semi-Riemannian submersions and Hopf fibrations. We also prove that U(2) with such a structure is foliated by Reinhart lightlike hypersurfaces. Finally, we consider a normal indefinite globally framed f-structure on the Lie group U(4) pro- ving that it projects on U(4)/U(3) in a Sasakian structure isomorphic to the standard Sasakian structure of S^7 |
| Handle: | http://hdl.handle.net/11586/1136 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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