A projective algebraic manifold M is a complex manifold in certain projective space CPm, m ≥ dimC M = n. The hyperplane line bundle of CPm restricts to an ample line bundle L onM . The bundle is a polarization onM . Suppose g is a Kähler metric on M . We say g is a polarized Kähler metric with respect to L, if the corresponding Kähler form represents the first Chern class c1(L) of L in H 2(M,Z)...

Let (E ,φ) be a flat Higgs bundle on a compact special affine manifold M equipped with an affine Gauduchon metric. We prove that (E ,φ) is polystable if and only if it admits an affine Yang–Mills–Higgs metric.

We consider the lift of a foliation to its conormal bundle and some transverse geometrical structures associated with this foliation are studied. We introduce a good vertical connection on the conormal bundle and, moreover, if the conormal bundle is endowed with a transversal Cartan metric, we obtain that the lifted foliation to its conormal bundle is a Riemannian one. Also, some transversally ...

We prove the existence of a (unique) S-invariant Ricci-flat Kähler metric on a neighbourhood of the zero section in the canonical bundle of a realanalytic Kähler manifold X, extending the metric on X. In the important paper [3], Calabi proved existence of Ricci-flat Kähler metrics on two classes of manifolds: a) cotangent bundles of projective spaces; b) canonical bundles of Kähler-Einstein man...

Abstract We consider a holomorphic family $f:\mathscr {X} \to S$ of compact complex manifolds and line bundle $\mathscr {L}\to \mathscr {X}$ . Given that {L}^{-1}$ carries singular hermitian metric has Poincaré type singularities along relative snc divisor {D}$ , the direct image $f_*(K_{\mathscr {X}/S}\otimes {D} \otimes {L})$ smooth metric. If {L}$ is relatively positive, we give an explicit ...

We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L 2 complex relative to a suitable metric on the bundle and a complete metric on the punctured Riemann surface. Applying results of C. Simpson, we show the existence of a harmonic metric on this vector bundle, giving the same L complex. As a ...