We construct non-flat non-Hermitian Yang--Mills connections with zero Einstein constant on smoothly trivial rank-two bundles over compact K\"ahler surfaces, with positive harmonic metrics and stable induced and adjoint holomorphic bundles. Thus vanishing Chern classes do not force flatness even under stability on both sides. The local model comes from a known complex anti-self-dual ansatz; the stable descents yield explicit global moduli phenomena. For a fixed stable bundle, the Kaledin--Verbitsky map contracts a complex line containing flat and non-flat points in the connected component of the Hermitian--Einstein connection. Contraction also occurs in the two-sided stable locus. The pair of holomorphic projections has a fibre containing both flat and non-flat points. An energy identity and a spectral-gap estimate quantify local flatness with the induced holomorphic structure fixed.
A long-standing conjecture in non-K\"ahler geometry states that a compact Hermitian manifold with constant Chern holomorphic sectional curvature should be K\"ahler when the constant is nonzero and Chern flat when the constant is zero. In this article, we study the corresponding problem for a Hermitian connection $\nabl...
In this paper, we prove several results concerning the function theory of complete Hermitian manifolds with vanishing Chern curvature, which we refer to as complete Chern-flat manifolds. First, we prove that any complete simply connected Chern-flat manifold is elliptic in the sense of Gromov. Moreover, it is biholomorp...
We formulate and solve a $G$-equivariant analogue of the Seiberg-Witten equations on any irreducible Hermitian symmetric space $G/K$. We use a canonical $K$-invariant form to define a twisted Hodge operator generalising self-duality to higher dimensions. The resulting equivariant Seiberg-Witten equations arise, for a c...
An old conjecture in Hermitian geometry states that a compact Hermitian manifold with constant holomorphic sectional curvature is K\"ahler when the constant is nonzero and Chern flat when the constant is zero. Yang--Zheng introduced the real bisectional curvature as a generalization of the holomorphic sectional curvatu...
Let $f$ be a holomorphic immersion from a compact complex hyperbolic space form into a higher-dimensional complex hyperbolic space form. We prove that if the normal bundle decomposes as a direct sum of holomorphic line bundles, then the immersion is totally geodesic. This result has no restriction on the codimension an...
We study the marked analytic moduli space of polystable degree-zero $\mathrm{SL}_r(\C)$-Higgs bundles over Teichm\"uller space. The connected components of the orbit-type loci defined by the full determinant-one stabilizers form a complex Whitney stratification. The projection to Teichm\"uller space is a holomorphic su...
Shi-Yu Cao· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
