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Yihong Hao

Publications and source records attributed to Yihong Hao.

5 recordsLinked to original sources
arXiv2026

The curvature estimation of the complete Kähler-Einstein metrics on the disk bundles

In this paper, we study some geometric properties of the disk bundles over the complete Kähler manifolds. When the base space is the complete Kähler-Einstein manifold, we compute the holomorphic sectional curvature, Riemannian sectional curvature of the complete Kähler-Einstein metric on the disk bundle. Moreover, we present a parametric criteria for whether the manifold admits negative pinched property. When the base space is a bounded pseudoconvex domain equipped with its complete Kähler metric, the corresponding ball bundle in the $k$-direct sum of line bundles is a bounded pseudoconvex Hartogs domain with fiber dimension $k$ . If the base domain is simply-connected and $k\geq2$, we prove that the Bergman metric on such a Hartogs domain is Kähler-Einstein if and only if the domain is biholomorphically equivalent to a unit ball.

math.CV↗
arXiv2026

The Kähler submanifolds between the ball bundles and the complex Euclidean space

In this paper, we provide a sufficient condition on the non-existence of the common Kähler submanifolds between the complex Euclidean space and the ball bundles of some Hermitian vector bundles over Kähler manifolds. Then we get the non-existence theorems on several classes of ball bundles whose base spaces are Hermitian symmetric spaces or the complete Kähler-Einstein manifolds.

math.CV↗
arXiv2020

Non-relativity of Kähler manifold and complex space forms

We study the non-relativity for two real analytic Kähler manifolds and complex space forms of three types. The first one is a Kähler manifold whose polarization of local Kähler potential is a Nash function in a local coordinate. The second one is the Hartogs domain equpped with two canonical metrics whose polarizations of the Kähler potentials are the diastatic functions.

math.CV↗
arXiv2014

Kähler geometry of bounded pseudoconvex Hartogs domains

Let $Ω$ be a bounded pseudoconvex Hartogs domain. There exists a natural complete Kähler metric $g^Ω$ in terms of its defining function. In this paper, we study two problems. The first one is determining when $g^Ω$ is Einstein or extremal. The second one is the existence of holomorphic isometric immersions of $(Ω, g^Ω)$ into finite or infinite dimensional complex space forms.

math.CV↗