For any Lagrangean Kähler submanifold M ⊂ T Cn, there exists a canonical hyper Kähler metric on T ∗M . A Kähler potential for this metric is given by the generalized Calabi Ansatz of the theoretical physicists Cecotti, Ferrara and Girardello. This correspondence provides a method for the construction of (pseudo) hyper Kähler manifolds with large automorphism group. Using it, a class of pseudo h...

The global holomorphic invariant αG(M) introduced by Tian[14], Tian and Yau[13] is closely related to the existence of Kähler-Einstein metrics. In his solution to the Calabi conjecture, Yau[19] proved the existence of a Kähler-Einstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is posi...

A Hermitian metric on a complex manifold of complex dimension n is called astheno-Kähler if its fundamental 2-form F satisfies the condition ∂∂F n−2 = 0 and it is strong KT if F is ∂∂-closed. We prove that a conformally balanced astheno-Kähler metric on a compact manifod of complex dimension n ≥ 3, whose Bismut connection has (restricted) holonomy contained in SU(n), is necessarily Kähler. We p...

We describe QCH Kähler surfaces $(M,g,J)$ of generalized orthotoric type. introduce a distinguished orthonormal frame on $(M,g)$ and give the structure equations for $(M,g,J)$. In case when opposite Hermitian $I$ is conformally

Let M = M̃/Γ be a Kähler manifold, where Γ ' π1(M) and where M̃ is the universal Kähler cover. Let (L, h) → M be a positive Hermitian holomorophic line bundle. We first prove that the L Szegő projector Π̃N for L holomorphic sections on the lifted bundle L̃ → M̃ is related to the Szegő projector for H(M,L ) by Π̂N (x, y) = ∑ γ∈Γ ̃̂ ΠN (γ · x, y). We apply this result to give a simple proof of Napier’s t...

1 Introduction The uniformalization of Kähler manifold has been an important topic in geometry for long. The famous Frankel Conjecture states: Compact n-dimensional Kähler Manifolds of Positive Bisectional Curvature are Bi-holomorphic to P n C. [10] by using stable harmonic maps in the context of Kähler geometry. Actually, Mori proved the Harthshorne Conjecture: Every irreducible n-dimensional ...

M-theory effects prevent five-dimensional domain-wall and black-hole solutions from developing curvature singularities. While so far this analysis was performed for particular models, we now present a model-independent proof that these solutions do not have naked singularities as long as the Kähler moduli take values inside the extended Kähler cone. As a by-product we obtain information on the ...

Our aim is to derive the effective action in four dimensions resulting by reducing dimensionally the ten-dimensional N = 1 heterotic supergravity coupled to N = 1 super Yang-Mills over manifolds admitting a nearly-Kähler structure. Given the fact that all homogeneous six-dimensional nearly-Kähler manifolds are included in the class of the corresponding non-symmetric coset spaces plus a group ma...

In this paper we first consider the Hamiltonian action of a compact connected Lie group on anH-twisted generalized complexmanifold M. Given such an action, we define generalized equivariant cohomology and generalized equivariant Dolbeault cohomology. If the generalized complex manifoldM satisfies the ∂∂-lemma, we prove that they are both canonically isomorphic to (Sg)⊗HH(M), where (Sg ) is the ...