  We generalize Demailly's construction of projective jet bundles and strictly
negatively curved pseudometrics on them to the logarithmic case. We establish
this logarithmic generalization explicitly via coordinates, just as Noguchi's
generalization of the jets used by Green-Griffiths. As a first application, we
give a metric proof for the logarithmic version of Lang's conjecture concerning
the hyperbolicity of complements of divisors in a semi-abelian variety as well
as for the corresponding big Picard theorem.
