Some remarks on Finsler vector bundles (Q2714300)

Let us denote by \(V\) a Minkowski space with the norm function \(f\), and by \(G_f = \{ A\in \text{GL} (V) : f(A\xi)= f(\xi)\}\). It is proved that \((V,f)\) is an inner product space if and only if the isometry group \(G_f\) is isomorphic to the orthogonal group \(O(n)\). Applying this to Finsler structures, the author obtains that a vector bundle modelled on a Minkowski space (see this notion in \textit{Y. Ichijyo}'s paper [J. Math. Kyoto Univ. 16, 639-652 (1976; Zbl 0342.53048)]) is a Riemannian vector bundle if and only if the isometry group is isomorphic to the orthogonal group \(O(n)\).