This ebook is ready the sunshine like (degenerate) geometry of submanifolds had to fill a spot within the normal concept of submanifolds. The becoming value of sunshine like hypersurfaces in mathematical physics, specifically their broad use in relativity, and intensely restricted info to be had at the basic idea of lightlike submanifolds, prompted the current authors, in 1990, to do collaborative study at the material of this ebook. in line with a chain of author's papers (Bejancu , Bejancu-Duggal [1,3], Dug gal , Duggal-Bejancu [1,2,3]) and several researchers, this quantity was once conceived and built in the course of the Fall '91 and Fall '94 visits of Bejancu to the collage of Windsor, Canada. the first distinction among the lightlike submanifold and that of its non degenerate counterpart arises on account that within the first case, the traditional vector package intersects with the tangent package deal of the submanifold. therefore, one fails to exploit, within the ordinary manner, the speculation of non-degenerate submanifolds (cf. Chen ) to outline the brought about geometric items (such as linear connection, moment basic shape, Gauss and Weingarten equations) at the mild like submanifold. a few paintings is understood on null hypersurfaces and degenerate submanifolds (see an up to date record of references on pages 138 and a hundred and forty respectively). Our technique, during this e-book, has the next awesome good points: (a) it's the first-ever try of an up to date info on null curves, lightlike hypersur faces and submanifolds, in keeping with the idea of non-degenerate submanifolds.
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