Abstract

For a standard Finsler F on a manifold M, the domain is the whole tangent bundle T M and the fundamental tensor g is positive-definite. However, in many cases, these two conditions hold in a relaxed form only, namely one has either a psuedo-Finsler metric or a conic Finsler metric. Our aim is twofold. First, we want to give an account of quite a few subtleties that appear under such generalizations, say, for conic pseudo-finsler metrics. Second, we aim to provide some criteria that determine when a pseudo-Finsler metric F obtained as a general homogeneous combination of Finsler metrics and one-forms is again a Finsler-metric -- or, more precisely, that the conic domain on which g remains positive-definite. Such a combination generalizes the known -metrics in different directions. Remarkably, classical examples of Finsler metrics are reobtained and extended, with explicit computations of their fundamental tensors