On the boundary behavior of the holomorphic sectional curvature of the Bergman metric

Para-Kahler tangent bundles of constant para-holomorphic sectional curvature

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

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. 

Kähler-Einstein metrics and compactifications of Cn

The study of holomorphic and isometric immersions of a Kähler manifold (M,g) into a Kähler manifold (N,G) started with Calabi. In his famous paper [3] he considered the case when the ambient space (N,G) is a complex space form, i.e. its holomorphic sectional curvature KN is constant. There are three types of complex space forms : flat, hyperbolic or elliptic according as the holomorphic section...

COMPLETE EINSTEIN-KÄHLER METRIC AND HOLOMORPHIC SECTIONAL CURVATURE ON YII(r, p;K)

The explicit complete Einstein-Kähler metric on the second type Cartan-Hartogs domain YII(r, p;K) is obtained in this paper when the parameter K equals p 2 + 1 p+1 . The estimate of holomorphic sectional curvature under this metric is also given which intervenes between −2K and − 2K p and it is a sharp estimate. In the meantime we also prove that the complete Einstein-Kähler metric is equivalen...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball