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
Examples of indefinite globally framed f-structures on compact Lie groups
PASTORE, Anna Maria
2012
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^7I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
