We study the Weil-Petersson geometry for holomorphic families of Riemann Surfaces equipped with the unique conical metric of constant curvature −1.

Let X be a compact complex manifold and L → X a positive holomorphic line bundle. Assume that Aut(X,L)/C× is discrete, where Aut(X,L) is the group of holomorphic automorphisms of the pair (X,L). Donaldson [D] has recently proved that if X admits a metric ω ∈ c1(L) of constant scalar curvature, then (X,L) is Hilbert-Mumford stable for k sufficiently large. Since Kähler-Einstein metrics have cons...

Let (M, g) be a complete non-compact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. We prove that M is holomorphically covered by a pseudoconvex domain in C which is homeomorphic to R, provided (M, g) has uniformly faster than linear average quadratic curvature decay.

In this paper we shall prove two theorems about extending holo-morphic mappings between complex manifolds. Both results involve extending such mappings across pseudo-concave boundaries. The first is a removable singularities statement for meromorphic mappings into compact K~ihler manifolds. The precise result and several illustrative examples are given in Section 1. The second theorem is a Hart...

Munteanu (Complex spaces in Finsler, Lagrange and Hamilton Geometries, Kluwer Academic Publishers, Dordrecht, 2004) defined the canonical connection associated to a strongly pseudoconvex complex Finsler manifold (M, F). We first prove that holomorphic sectional curvature tensors of coincide with those Chern–Finsler F if only is Kähler-Finsler metric. also investigate relationship Ricci curvatur...

B.Y. Chen [3] established a sharp inequality for the warping function of a warped product submanifold in a Riemannian space form in terms of the squared mean curvature. For a survey on warped product submanifolds we refer to [4]. In [8], we established a similar relationship between the warping function f (intrinsic structure) and the squared mean curvature and the holomorphic sectional curvatu...

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...