Positively curved Finsler metrics on vector bundles II

We show that if E is an ample vector bundle of rank at least two with some curvature bound on OP(E∗)(1), then E∗⊗detE is Kobayashi positive. The proof relies on comparing the curvature of (detE∗)k and SkE for large k and using duality of convex Finsler metrics. Following the same thread of thought, we show if E is ample with similar curvature bounds on OP(E∗)(1) and OP(E⊗detE∗)(1), then E is Kobayashi positive. With additional assumptions, we can furthermore show that E∗⊗detE and E are Griffiths positive.