CONNECTIONS ON ALMOST COMPLEX FINSLER MANIFOLDS AND KOBAYASHI HYPERBOLICITY

Estimates of the Kobayashi Metric on Almost Complex Manifolds

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold (M, J) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in (M, J). Finally we obtain the regul...

Estimates of the Kobayashi-royden Metric in Almost Complex Manifolds

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold (M, J) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in (M, J).

On Stretch curvature of Finsler manifolds

In this paper, Finsler metrics with relatively non-negative (resp. non-positive), isotropic and constant stretch curvature are studied.  In particular, it is showed that every compact Finsler manifold with relatively non-positive (resp. non-negative) stretch curvature is a Landsberg metric. Also, it is proved that every  (α,β)-metric of non-zero constant flag curvature and non-zero relatively i...

Schwarz-type lemmas for solutions of ¯∂-inequalities and complete hyperbolicity of almost complex manifolds.

Gromov hyperbolicity and the Kobayashi metric

It is well known that the unit ball endowed with the Kobayashi metric is isometric to complex hyperbolic space and in particular is an example of a negatively curved Riemannian manifold. One would then suspect that when Ω ⊂Cd is a domain close to the unit ball then (Ω ,KΩ ) should be negatively curved (in some sense). Unfortunately, for general domains the Kobayashi metric is no longer Riemanni...