Xi Zhang

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math.DG2025

Homogeneous hypersurfaces of the four-dimensional Thurston geometry $So l_{0}^{4}$

Marie D'haene, Guoxin Wei, Zeke Yao +1

In this paper, we classify hypersurfaces with constant principal curvatures in the four-dimensional Thurston geometry $So l_{0}^{4}$ under certain geometric conditions. As an appl…

math.DG2025

Hermitian-Poisson metrics on projectively flat complex vector bundles over non-compact Gauduchon manifolds

Jie Geng, Zhenghan Shen, Xi Zhang

In this paper, we investigate the projectively flat bundles over a class of non-compact Gauduchon manifolds. By combining heat flow techniques and continuity methods, we establish…

math.DG2024

Liouville theorem for $V$ -harmonic heat flows

Han Luo, Weike Yu, Xi Zhang

In this paper, we investigate $V$ -harmonic heat flows from complete Riemannian manifolds with nonnegative Bakry-Emery Ricci curvature to complete Riemannian manifolds with sectiona…

Homogeneous hypersurfaces of the four-dimensional Thurston geometry Sol04​

Hermitian-Poisson metrics on projectively flat complex vector bundles over non-compact Gauduchon manifolds

Liouville theorem for V-harmonic heat flows

Homogeneous hypersurfaces of the four-dimensional Thurston geometry $So l_{0}^{4}$

Liouville theorem for $V$ -harmonic heat flows