Abstract
Let X be a reduced compact complex space and E→X a ⊄-linear fibre space. Let P(E) be the associated projective variety over X and let L(E) be the canonical line bundle over P(E). Generalizing a result of Kobayashi, we prove that E carries a Finsler metric of negative curvature if and only if L(E)red→P(E)red carries an Hermitian metric of negative curvature.
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