A locally symmetric Kähler Einstein structure on the tangent bundle of a space form.
A Nakai-Moishezon criterion for non-Kähler surfaces
A version of the classical Nakai-Moishezon criterion is proved for all compact complex surfaces, regardless of the parity of the first Betti number.
A new proof of the existence of Kähler-Einstein metrics on A3, II.
A new proof of the existence of Kähler-Einstein metrics on K3, I.
A Note on compact Kähler manifolds with Nef Tangent Bundles.
A pseudo-Riemannian metric on the tangent bundle of a Riemannian manifold.
A recurrent curvature-like tensor on semi-definite Kähler manifolds.
A Reduction Theorem for Cohomology Groups of Very Strongly q-convex Kähler Manifolds.
A remark on compact symplectic manifolds not admitting complex structures
A remark on four-dimensional almost Kähler-Einstein manifolds with negative scalar curvature.
A Riemann-Roch-Hirzebruch formula for traces of differential operators
Let be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an -dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology of the algebra of differential operators on a formal neighbourhood of a...
A rigidity property of class VIIo surface fundamental groups.
A series of Kählerian invariants and their applications to Kählerian geometry.
A Simple Proof of the Subjectivity of the Period Map of K3 Surfaces.
A survey on axioms of submanifolds in Riemannian and Kaehlerian geometry
A Tensorial Curvature and a Theorem of Chern.
A Twistor Description of Harmonic Maps of a 2-Sphere into a Grassmannian.
A unified approach to some theorems on homogeneous Riemannian and affine spaces
About the Calabi problem: a finite-dimensional approach
Let us consider a projective manifold and a smooth volume form on . We define the gradient flow associated to the problem of -balanced metrics in the quantum formalism, the -balancing flow. At the limit of the quantization, we prove that (see Theorem 1) the -balancing flow converges towards a natural flow in Kähler geometry, the -Kähler flow. We also prove the long time existence of the -Kähler flow and its convergence towards Yau’s solution to the Calabi conjecture of prescribing the...
Affine compact almost-homogeneous manifolds of cohomogeneity one
This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem...