A Schwarz lemma for weakly Kähler-Finsler manifolds

A General Schwarz Lemma for Almost-hermitian Manifolds

We prove a version of Yau’s Schwarz Lemma for general almost-complex manifolds equipped with almost-Hermitian metrics. This requires an extension to this setting of the Laplacian comparison theorem. As an application we show that the product of two almost-complex manifolds does not admit any complete almost-Hermitian metric with bisectional curvature bounded between two negative constants that ...

Kähler (& Hyper-kähler) Manifolds

These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...

A Schwarz Lemma for Correspondences and Applications

A version of the Schwarz lemma for correspondences is studied. Two applications are obtained namely, the ‘non-increasing’ property of the Kobayashi metric under correspondences and a weak version of the Wong-Rosay theorem for convex, finite type domains admitting a ‘non-compact’ family of proper correspon-

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...

Stable Exponentially Harmonic Maps Between Finsler Manifolds