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...
Almost Complex Manifolds and Hirzebruch Invariant for Isolated Singularities in Complex Spaces.
Almost contact metric 3-submersions.
Almost hermitian geometry on six dimensional nilmanifolds
Almost Hermitian surfaces with vanishing Tricerri-Vanhecke Bochner curvature tensor
We study the curvature properties of almost Hermitian surfaces with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. Local structure theorems for such almost Hermitian surfaces are provided, and several examples related to these theorems are given.
Almost hyper-Hermitian structures in bundle spaces over manifolds with almost contact -structure
We consider almost hyper-Hermitian structures on principal fibre bundles with one-dimensional fiber over manifolds with almost contact 3-structure and study relations between the respective structures on the total space and the base. This construction suggests the definition of a new class of almost contact 3-structure, which we called trans-Sasakian, closely connected with locally conformal quaternionic Kähler manifolds. Finally we give a family of examples of hypercomplex manifolds which are not...