We introduce the weighted orthogonal Ricci curvature – a two-parameter version of Ni–Zheng's curvature. This serves as very natural object in study relationship between curvature(s) and holomorphic sectional In particular, determining optimal constraints for compact Kähler manifold to be projective. this direction, we prove number vanishing theorems using both Hermitian category.

The notion of holomorphic bi-flag curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is devoted to obtain the characterizations of the holomorphic bi-flag curvature. For the class of generalized...

in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.

We prove a sharp lower bound for the Tanaka–Webster holomorphic sectional curvature of strictly pseudoconvex real hypersurfaces that are “semi-isometrically” immersed in Kähler manifold nonnegative under an appropriate

Let (M, g) be a simply connected complete Kähler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in Cn, where dimCM = n. Résumé. Soit (M, g) une variété kählérienne complète et simplement connexe à courbure sectionnelle non-positive. Supposons que g ai...

Let (M, g, J) be a compact Hermitian manifold with a smooth boundary. Let ∆p,B and ⊓ ⊔p,B be the realizations of the real and complex Laplacians on p forms with either Dirichlet or Neumann boundary conditions. We generalize previous results in the closed setting to show that (M, g, J) is Kaehler if and only if Spec(∆p,B) = Spec(2 ⊓ ⊔p,B) for p = 0, 1. We also give a characterization of manifold...

In this paper, we derive a partial result related to a question of Professor Yau: “Does a simply-connected complete Kähler manifold M with negative sectional curvature admit a bounded non-constant holomorphic function?” Main Theorem. Let M be a simply-connected complete Kähler manifold M with negative sectional curvature ≤ −1 and S∞(M) be the sphere at infinity of M . Then there is an explicit ...

In this work, we obtain a existence criteria for the longtime K\ahler Ricci flow solution. Using result, generalize result by Wu-Yau on of Einstein metric to case with possibly unbounded curvature. Moreover, negative scalar curvture must be unique up scaling.