Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

This work has been written with a two-fold approach in mind: firstly, it adds to the theory of submanifolds the missing part of lightlike (degenerate) submanifolds of semi-Riemannian manifolds, and, secondly, it applies relevant mathematical results to branches of physics. It presents important results on null curves, lightlike hypersurfaces and their applications to relativistic electromagnetism, radiation fields, killing horizons and asymptotically flat spacetimes in a consistent way. Many differences between non-degenerate and degenerate geometry are highlighted, and open problems for both mathematicians and physicists are given.