Kähler manifolds and their relatives

Ja n 20 06 Kähler manifolds and their relatives

Let M 1 and M 2 be two Kähler manifolds. We call M 1 and M 2 relatives if they share a non-trivial Kähler submanifold S, namely, if there exist two holomorphic and isometric immersions (Kähler immersions) h 1 : S → M 1 and h 2 : S → M 2. Moreover, two Kähler manifolds M 1 and M 2 are said to be weakly relatives if there exist two locally isometric (not necessarily holomorphic) Kähler manifolds ...

Kähler manifolds and their relatives

Let M1 and M2 be two Kähler manifolds. We call M1 and M2 relatives if they share a non-trivial Kähler submanifold S, namely, if there exist two holomorphic and isometric immersions (Kähler immersions) h1 : S → M1 and h2 : S → M2. Moreover, two Kähler manifolds M1 and M2 are said to be weakly relatives if there exist two locally isometric (not necessarily holomorphic) Kähler manifolds S1 and S2 ...

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...

Strictly Kähler-Berwald manifolds with constant‎ ‎holomorphic sectional curvature

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

One Introduction to Kähler Manifolds