Lightlike Hypersurfaces of Lorentz Framed Manifolds
In the previous Chapter 6, we studied a class of lightlike submanifolds of Kaehler manifolds which are necessarily even dimensional. In this chapter, we consider a more general ambient manifold, called framed manifold of even as well as odd dimension. The reader will soon know why we concentrate on Lorentz manifolds. In section 7.1, we brief the needed information on the framed structure of a Lorentz manifold, which is then used, in section 7.2, to construct a class of invariant lightlike framed hypersurfaces. Section 7.3 is devoted to the study of a large class of lightlike framed hypersurfaces of globally hyperbolic spacetimes. In particular, we show that Minkowski and extended Schwarzchild spacetimes can be endowed with a framed structure and these spaces do have lightlike hypersurfaces with induced framed structure.
KeywordsRiemannian Manifold Lorentz Manifold Spacelike Hypersurface Product Manifold Kill Vector Field
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