Related papers: K\"ahler-Einstein metrics and obstruction flatness…

In this paper, we investigate analytic and geometric properties of obstruction flatness of strongly pseudoconvex CR hypersurfaces of dimension $2n-1$. Our first two results concern local aspects. Theorem 3.2 asserts that any strongly…

This work treats on the question whether a given map f: M -> B of smooth closed manifolds is homotopic to a smooth fiber bundle. We define a first obstruction in H^1(B;Wh(\pi_1(E))) and, provided that this obstruction vanishes and one…

We study the K\"ahler-Ricci flow on a class of projective bundles $\mathbb{P}(\mathcal{O}_\Sigma \oplus L)$ over compact K\"ahler-Einstein manifold $\Sigma^n$. Assuming the initial K\"ahler metric $\omega_0$ admits a U(1)-invariant momentum…

We describe two simple obstructions to the existence of Ricci-flat Kahler cone metrics on isolated Gorenstein singularities or, equivalently, to the existence of Sasaki-Einstein metrics on the links of these singularities. In particular,…

We study horizontal deformations of a Higgs bundle whose spectral curve is smooth. It allows us to define a natural integrable connection of the Hitchin fibration on the locus where the spectral curves are smooth. Then, in the non-zero…

We study the conditions under which the cotangent bundle $T^*M$ of a Riemaannian manifold $(M,g)$, endowed with a K\"ahlerian structure $(G,J)$ of general natural lift type (see \cite{Druta1}), is Einstein. We first obtain a general natural…

It is a classical fact that the cotangent bundle $T^* \M$ of a differentiable manifold $\M$ enjoys a canonical symplectic form $\Omega^*$. If $(\M,\j,g,\omega)$ is a pseudo-K\"ahler or para-K\"ahler $2n$-dimensional manifold, we prove that…

We consider a notion of balanced metrics for triples (X,L,E) which depend on a parameter \alpha, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of \alpha, we…

In this paper we give a criterion for a deformation of a hermitian vector bundle to be Ricci-flat. As an application we show that on a K\"ahler manifold, every deformation of a vector bundle can be made Ricci-flat whereas on some Hopf…

In this paper, we study numerically flat holomorphic vector bundles over a compact non-K\"ahler manifold $(X, \omega)$ with the Hermitian metric $\omega$ satisfying the Gauduchon and Astheno-K\"ahler conditions. We prove that numerically…

The moduli space of stable Higgs bundles of degree $0$ is equipped with the hyperk\"ahler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperk\"ahler metric called the semi-flat metric,…

This work seeks to advance the understanding of the smooth structure of the moduli space of self-dual contact instantons (SDCI) on Sasakian 7-manifolds M. A neighborhood of a smooth point of M is locally modeled on the first cohomological…

We study the conditions under which the tangent bundle $(TM,G)$ of an $n$-dimensional Riemannian manifold $(M,g)$ is conformally flat, where $G$ is a general natural lifted metric of $g$. We prove that the base manifold must have constant…

We find a family of K\"ahler metrics invariantly defined on the radius $r_0>0$ tangent disk bundle ${{\cal T}_{M,r_0}}$ of any given real space-form $M$ or any of its quotients by discrete groups of isometries. Such metrics are complete in…

We adapt the notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles for canonically polarized framed manifolds, i.e. compact complex manifolds X…

A twisted Higgs bundle on a K\"ahler manifold $X$ is a pair $(E,\phi)$ consisting of a holomorphic vector bundle $E$ and a holomorphic bundle morphism $\phi\colon M\otimes E \to E$ for some holomorphic vector bundle $M$. Such objects were…

A differential operator introduced by A. Gray on the unit sphere bundle of a K\"ahler-Einstein manifold is studied. A lower bound for the first eigenvalue of the Laplacian for the Sasaki metric on the unit sphere bundle of a…

Given a compact Riemann surface $\Sigma$ of genus $g_\Sigma\, \geq\, 2$, and an effective divisor $D\, =\, \sum_i n_i x_i$ on $\Sigma$ with $\text{degree}(D)\, <\, 2(g_\Sigma -1)$, there is a unique cone metric on $\Sigma$ of constant…

Let $M$ a compact connected orientable 4-manifold. We study the space $\Xi$ of $Spin^c$-structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on $M$. In order to study…

In this paper, we investigate the existence of weak singular Hermite-Einstein structures on homogeneous holomorphic vector bundles over rational homogeneous varieties. Using Cartan's highest weight theory, we establish an explicit algebraic…