Xiaokui Yang

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20232025

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math.DG2025

Chern number identities on compact complex surfaces and applications

Xiaokui Yang

In this paper, we establish Chern number identities on compact complex surfaces. As an application, we prove that if $(M, g)$ is a compact Riemannian four-manifold with constant sca…

math.DG2025

Conformal extremal metrics and constant scalar curvature

Xiaokui Yang, Kaijie Zhang

Let $M$ be a compact complex manifold of dimension $n \geq 2$ . We prove that for any Hermitian metric $ω$ on $M$ , there exists a unique smooth function $f$ (up to additive constants…

math.DG2024

Manifolds with non-positive second Chern-Ricci curvature

Xiaokui Yang

In this paper, we establish a Kählerian or projectivity criterion for a class of compact Hermitian surfaces with non-positive second Chern-Ricci curvature.

math.DG2023

New curvature characterizations for spherical space forms and complex projective spaces

Xiaokui Yang, Liangdi Zhang

In this paper, we introduce a new positivity notion for curvature of Riemannian manifolds and obtain characterizations for spherical space forms and the complex projective space $\…