GENERALIZED HOLOMORPHIC CARTAN GEOMETRIES

Recall that a compact K¨ ahler manifold of odd complex dimension bearing a holomor- phic SL(2, C )–structure also admits a holomorphic Riemannian metric and inherits of the

Les vari´ et´ es LVMB [10, 11, 3, 4] (voir aussi [14]) forment une classe de vari´ et´ es complexes compactes (en g´ en´ eral, non–K¨ ahler) qui g´ en´ eralise les vari´ et´

In this paper, we prove that the Grothendieck-Riemann-Roch formula in Deligne co- homology computing the determinant of the cohomology of a holomorphic vector bundle on the fibers of

Given a compact complex n-fold X satisfying the ∂ ∂-lemma and sup- ¯ posed to have a trivial canonical bundle K X and to admit a balanced (=semi- K¨ ahler) Hermitian metric ω,

— Given a compact complex n-fold X satisfying the ∂ ∂-lemma and ¯ supposed to have a trivial canonical bundle K X and to admit a balanced (=semi- Kähler) Hermitian metric ω,

Conversely the author [1, Theorem 3] proved that an open set D of a Stein manifold X of dimension two is Stein if every holomorphic line bundle L on D is associated to some

n-dimensional g.H.. We shall investigate harmonic forms with respect to U and get the complex version of Theorem 2.3. Namely we show the following theorem...

Roughly speaking, this theorem states that, if the integrable vector field which is to be perturbed is nondegenerate in some sense and if the perturbation is small enough and