Abstract
In this chapter we present a review of differentiable manifolds, tensor fields, covariant and exterior derivatives and linear connection. Using the Levi-Civita connection we brief on the geometry of semi-Riemannian manifolds and their non-degenerate hypersurfaces. In the last two sections we deal with the basic results on null curves and lightlike hypersurfaces of 4 dimensional Lorentz manifolds. On null curves we show the existence of an affine parameter and its Frenet frame, consisting of two real null and two spacelike vectors. We prove the existence of Levi-Civita induced connection on totally geodesic lightlike hypersurfaces. The main formulas and results are expressed by using both the invariant form and the index form.
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