Lightlike hypersurfaces in indefinite $\mathcal{S}$-manifolds

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In a metric $g.f.f$-manifold we study lightlike hypersurfaces $M$ tangent to the characteristic vector fields, and owing to the presence of the $f$-structure, we determine some decompositions of $TM$ and of a chosen screen distribution obtaining two distributions invariant with respect to the structure. We discuss the existence of a $g.f.f$-structure on a lightlike hypersurface and, under suitable hypotheses, we obtain an indefinite $\mathcal{S}$-structure on the leaves of an integrable distribution. The existence of totally umbilical lightlike hypersurfaces of an indefinite $\mathcal{S}$-space form is also discussed. Finally, we explicitely describe a lightlike hypersurface of an indefinite $\mathcal{S}$-manifold.
19 pages, no figures

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Differential Geometry, 53C40; 53C50; 53D10

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http://salesiana.dossiersoluciones.com/handle/123456789/157549

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.3896
 http://arxiv.org/abs/0803.3896

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arXiv