Strictly non-proportional geodesically equivalent metrics have htop(g)=0h_\text{top}(g)=0

Suppose the Riemannian metrics $g$ and $\bar g$ on a closed connected manifold $M^n$ are geodesically equivalent and strictly non-proportional at least at one point. Then the topological entropy of the geodesic flow of $g$ vanishes.Comment: This is a slightly extended version of the paper submitted to ETDS. 16 pages, one .eps figur

The Kobayashi pseudodistance on almost complex manifolds

We extend the definition of the Kobayashi pseudodistance to almost complex manifolds and show that its familliar properties are for the most part preserved. We also study the automorphism group of an almost complex manifold and finish with some examples.Comment: 19 pages, Late