An isometric immersion f : Mn ? ?Mm from an n-dimensional Riemannian manifold into almost Hermitian of complex dimension m is called pointwise slant if its Wirtinger angles define a function defined on Mn. In this paper we establish the Existence and Uniqueness Theorems for immersions manifolds space form ?Mn(c) constant holomorphic sectional curvature c, which extend proved by B.-Y. Chen L. Vr...

Let (M, g) be a complete non compact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. Extending our techniques developed in [8], we prove that the universal cover M̃ of M is biholomorphic to Cn provided either that (M, g) has average quadratic curvature decay, or M supports an eternal solution to the Kähler-Ricci flow with non-negative and uniformly bounded holomo...

We investigate the property of the Wu invariant metric on a certain class of psuedoconvex domains. We show that the Wu invariant Hermitian metric, which in general behaves as nicely as the Kobayashi metric under holomorphic mappings, enjoys the complex hyperbolic curvature property in such cases. Namely, the Wu invariant metric is Kähler and has constant negative holomorphic curvature in a neig...

We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.

Let π : X → B be a holomorphic submersion between compact Kähler manifolds of any dimensions, whose fibres and base have no non-zero holomorphic vector fields and whose fibres admit constant scalar curvature Kähler metrics. This article gives a sufficient topological condition for the existence of a constant scalar curvature Kähler metric on X. The condition involves the CM-line bundle—a certai...

1. Statement of the results. 1.1. Let M be a compact Kaehlerian manifold. The underlying Riemannian manifold which we also denote by M is orientable and of even dimension. Let K = K(<r) be the Riemannian curvature of M, considered as a Riemannian manifold. K(a) is a function on the 2planes a tangent to M. The restriction of K to holomorphic 2-planes is called holomorphic curvature and will be d...