相关论文: Hamiltonian 2-forms in Kahler geometry, IV Weakly …

In this short note we prove that a Kahler manifold with lower Ricci curvature bound and almost maximal volume is Gromov-Hausdorff close to the projective space with the Fubini-Study metric. This is done by combining the recent results of…

In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach-Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein-Maxwell…

We study many properties concerning weak K\"ahlerianity on compact complex manifolds which admits a holomorphic submersion onto a K\"ahler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the K\"ahler…

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.

We give an account of old and new results concerning many types of non-K\"ahler metrics, with focus on the problem of their coexistence on compact complex manifolds, and their behaviour at deformations and blow-up. We also describe a…

We classify compact self-dual almost-K\"ahler four manifolds of positive type and zero type. In particular, using LeBrun's result, we show that any self-dual almost-K\"ahler metric on a manifold which is diffeomorphic to $\mathbb{CP}_{2}$…

In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets…

We study holomorphic 2-forms on projective (or compact Kaehler) threefolds not of general type and prove that in almost all cases the 2-form is created by some standard process. This means roughly that every 2-form is induced by a…

For a compact relative K\"ahler fibration over a compact K\"ahler manifold with negative holomorphic sectional curvature, if the relative K\"ahler form on each fiber also exhibits negative holomorphic sectional curvature, we can construct…

We construct explicit examples of quaternion-K\"ahler and hypercomplex structures on bundles over hyperK\"ahler manifolds. We study the infinitesimal symmetries of these examples and the associated Galicki-Lawson quaternion-K\"ahler moment…

We show the existence of strictly almost-Kahler anti-self-dual metrics on certain 4-manifolds by deforming scalar-flat Kahler metrics. On the other hand, we prove the non-existence of such metrics on certain other 4-manifolds by means of…

In a recent paper Donaldson explains how to use an older construction of Joyce to obtain four dimensional local models for scalar-flat Kahler metrics with a 2-torus symmetry. Using this idea, he recovers and generalizes the Taub-NUT metric…

In this paper the classification of left-invariant Riemannian metrics, up to the action of the automorphism group, on cotangent bundle of (2n+1)-dimensional Heisenberg group is presented. Also, it is proved that the complex structure on…

Using examples of compact complex 3-manifolds which arise as twistor spaces, we show that the class of compact complex manifolds bimeromorphic to K\"ahler manifolds is not stable under small deformations of complex structure.

We present three families of exact, cohomogeneity-one Einstein metrics in $(2n+2)$ dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of…

A weak metric $f$-structure $(f,Q,\xi_i,\eta^i,g)\ (i=1,\ldots,s)$, generalizes the metric $f$-structure on a smooth manifold, i.e., the complex structure on the contact distribution is replaced with a nonsingular skew-symmetric tensor. We…

We derive a formula for the L^2 norm of the scalar curvature of any extremal Kaehler metric on a compact toric manifold, stated purely in terms of the geometry of the corresponding moment polytope. The main interest of this formula pertains…

The conformal properties of complex Finsler metrics are studied. We give a characterization of a compact complex Finsler manifold to be globally conformal K\"ahler. The critical points of the total holomorphic curvature and total Ricci…

We show that for all very special quaternionic manifolds a different N=1 reduction exists, defining a Kaehler Geometry which is ``dual'' to the original very special Kaehler geometry with metric G_{a\bar{b}}= - \partial_a \partial_b \ln V…

Let (X,\Omega) be a closed polarized complex manifold, g be an extremal metric on X that represents the K\"ahler class \Omega, and G be a compact connected subgroup of the isometry group Isom(X,g). Assume that the Futaki invariant relative…