相关论文: Complete Einstein-K\"{a}hler Metric and Holomorphi…

In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are…

We study equivalence of invariant metrics on noncompact K\"ahler manifolds with a complete Bergman metric of bounded curvature. Especially only the boundedness of the ratio between Bergman kernel and the $n$-times wedge product of Bergman…

We calculate the $L^2$-norm of the holomorphic sectional curvature of a K\"ahler metric by representation-theoretic means. This yields a new proof that the holomorphic sectional curvature determines the whole curvature tensor. We then…

We prove that a complete K\"ahler manifold with holomorphic curvature bounded between two negative constants admits a unique complete K\"ahler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly…

We show the theorem which provides some sufficient condition to the non-existence of a complete K\"ahler--Einstein metric of negative scalar curvature whose holomorphic sectional curvature is negatively pinched: Let $\Omega$ be a bounded…

The subject of this paper is the explicit momentum construction of complete Einstein metrics by ODE methods. Using the Calabi ansatz, further generalized by Hwang-Singer, we show that there are non-trivial complete conformally K\"ahler…

Grauert showed that the existence of a complete K\"{a}hler metric does not characterize domains of holomorphy by constructing such metrics on the complements of complex analytic sets in a domain of holomorphy. In this note, we study the…

Any $6$-dimensional strict nearly K\"ahler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we…

The object of the present paper is to study some properties of para-K$\"{a}$hler manifold whose metric is conformal Einstein soliton. We have studied some certain curvature properties of para-K$\"{a}$hler manifold admitting conformal…

Let $L$ be a negative holomorphic line bundle over an $(n-1)$-dimensional complex torus $D$. Let $h$ be a Hermitian metric on $L$ such that the curvature form of the dual Hermitian metric defines a flat K\"ahler metric on $D$. Then $h$ is…

In this short note we are concerned with the Kahler-Einstein metrics near cone type log canonical singularities. By two different approaches, we construct a complete Kahler-Einstein metric with negative scalar curvature in a neighborhood of…

Let $\mathcal{H}_{n,k}(\Sigma)$ be the space of degree $n\geq 1$ holomorphic maps from a compact Riemann surface $\Sigma $ to $\mathbb{C}P^k$. In the case $\Sigma=S^2$ and $n=1$, the $L^2$ metric on $\mathcal{H}_{1,k}(S^2)$ was computed…

In this paper, we study constant scalar curvature K\"ahler (cscK) metrics on complete non-compact K\"ahler--Einstein manifolds. We give sufficient conditions under which a cscK perturbation of a K\"ahler--Einstein metric must remain…

We study Hermitian metrics with constant second scalar curvature on compact manifolds. We first consider a Yamabe-type problem for the second Bismut scalar curvature under a natural topological condition, and then analyze elliptic equations…

Inspired by a parabolic system of Li-Yuan-Zhang and the continuity equation of La Nave-Tian, we study a system of elliptic equations for a K\"ahler metric $\omega$ and a closed $(1, 1)$-form $\alpha$. Assuming a uniform estimate for…

In this paper, first of all, according to Lu's and Zhang's works about the curvature of the Bergman metric on a bounded domain and the properties of the squeezing functions, we obtain that Bergman curvature of the Bergman metric on a…

Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…

We introduce a natural extension of the metric tensor and the Hodge star operator to the algebra of double forms to study some aspects of the structure of this algebra. These properties are then used to study new Riemannian curvature…

We study the integrability to second order of infinitesimal Einstein deformations on compact Riemannian and in particular on K\"ahler manifolds. We find a new way of expressing the necessary and sufficient condition for integrability to…

We show the existence of complete negative K\"ahler-Einstein metric on Stein manifolds with negatively pinched holomorphic sectional curvature. We prove that any K\"ahler metrics on such manifolds can be deformed to the complete negative…