In this article, we study the higher-order regularity of Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. By developing sharp new parabolic Schauder estimates cylinders, proved that when generic fibers Iitaka fibration are biholomorphic to each other, converges in C loc ? -topology away from singular a negative Kähler-Einstein metric base manifold. particular...

We compute the moduli metrics of worldvolume 0-brane solitons of D-branes and the worldvolume self-dual string solitons of the M-5-brane and examine their geometry. We find that the moduli spaces of 0-brane solitons of D-4-branes and D-8-branes are hyper-Kähler manifolds with torsion and octonionic Kähler manifolds with torsion, respectively. The moduli space of the self-dual string soliton of ...

Link invariants, for 3-manifolds, are defined in the context of the RozanskyWitten theory. To each knot in the link one associates a holomorphic bundle over a holomorphic symplectic manifold X . The invariants are evaluated for b1(M) ≥ 1 and X Hyper-Kähler. To obtain invariants of Hyper-Kähler X one finds that the holomorphic vector bundles must be hyper-holomorphic. This condition is derived a...

We generalize the notions of the Futaki invariant and extremal vector field of a compact Kähler manifold to the general almost-Kähler case and show the periodicity of the extremal vector field when the symplectic form represents an integral cohomology class modulo torsion. We also give an explicit formula of the hermitian scalar curvature in Darboux coordinates which allows us to obtain example...

We study some subsets of the Green-Lazarsfeld set Σ1(M) for a compact Kähler manifold M .

Let X be a 2n−dimensional smooth manifold. A 2−form ω on X is said to be non-degenerate if, for each q ∈ X and for each nonzero vector v in the tangent space TqX, there is a tangent vector v ∈ TqX such that ω(u, v) 6= 0. A symplectic structure onX is a non-degenerate closed 2−form. The fundamental example of a symplectic structure is ω0 = ∑ i dxi ∧ dyi on R = {(x1, y1, ..., xn, yn)}. In fact, b...

It is shown that the first order (Palatini) variational principle for a generic nonlinear metric-affine Lagrangian depending on the (symmetrized) Ricci square invariant leads to an almost-product Einstein structure or to an almost-complex anti-Hermitian Einstein structure on a manifold. It is proved that a real anti-Hermitian metric on a complex manifold satisfies the Kähler condition on the sa...

We study the structure of warped compactifications of type IIB string theory to six space–time dimensions. We find that the most general four-manifold describing the internal dimensions is conformal to a Kähler manifold, in contrast with the heterotic case where the four-manifold must be conformally Calabi–Yau.  2004 Elsevier B.V. All rights reserved.

1.1. Log-K-stability Let (X, J) be a Fano manifold, that is, K−1 X is ample. A basic problem in Kähler geometry is to determine whether (X, J) has a Kähler–Einstein metric (see [22]). The existence problem of Kähler–Einstein metric is a special case of the existence problem of constant scalar curvature Kähler (cscK) metric. For the latter, we fix an ample line bundle L on (X, J). We have the fo...