In this talk we will be discussing an attempt to define a Kobayashi metric on a riemannian manifold using local harmonic maps from disks in the plane, namely a real analogue of Kobayashi metric on a complex manifold. In particular, we will show that the (real) Kobayashi metric of the Poincare disk (as a riemannian manifold) is identically zero, a dramatic turn from the (complex) Kobayashi metric of the unit disk, which is the Poincare metric on the unit disk.

海报