相关论文: Bihermitian metrics on Hopf surfaces

In this paper, we study several types of geometric problems related to the Ricci curvature on noncompact complex manifolds, such as the existence of K\"{a}hler-Einstein metrics on complete K\"{a}hler manifolds with negative Ricci curvature,…

In this paper, we construct infinitely many bi-invariant metrics on the Hamiltonian diffeomorphism group and study their basic properties and corresponding generalizations of the Hofer inequality and Sikorav one.

We show that any hyperbolic Inoue surface (or Inoue-Hirzebruch surface of even type) admits anti-self-dual bihermitian structures. The same result also holds for any of its small deformations as far as its anti-canonical system is…

In this work we obtain some geometric properties of biconservative surfaces into a Riemannian manifold. In particular, we shall study the relationship between biconservative surfaces and the holomorphicity of a generalized Hopf function.…

Oeljeklaus-Toma (OT) manifolds are higher dimensional analogues of Inoue-Bombieri surfaces and their construction is associated to a finite extension $K$ of $Q$ and a subgroup of units $U$. We characterize the existence of pluriclosed…

It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as…

In this paper, we provide new examples of Levi-Civita Ricci-flat Hermitian metrics on certain compact non-K\"{a}hler Calabi-Yau manifolds, including every compact Hermitian Weyl-Einstein manifold, every compact locally conformal…

We construct smooth Riemannian metrics with constant scalar curvature on each Hirzebruch surface. These metrics respect the complex structures, fiber bundle structures, and Lie group actions of cohomogeneity one on these manifolds. Our…

We study complex non-K\"ahler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed…

We introduce a class of hermitian metrics with {\em Lee potential}, that generalize the notion of l.c.K. metrics with potential introduced in \cite{ov} and show that in the classical examples of Calabi and Eckmann of complex structures on…

Let M be a compact complex surface which admits a Kaehler metric whose scalar curvature has integral zero; and suppose the fundamental group of M does not contain an Abelian subgroup of finite index. Then if M is blown up at sufficiently…

Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.

We construct a family of Hermitian metrics on the Hopf surface $ \mathbb{S}^3\times \mathbb{S}^1$, whose fundamental classes represent distinct cohomology classes in the Aeppli cohomology group. These metrics are locally conformally…

We show the existence of Gauduchon metrics on arbitrary compact hermitian varieties, generalizing our previous work on smoothable singularities. These metrics allow us to define the notion of slope stability for torsion-free coherent…

Motivated by a recent work of Chen-Zheng [8] on Strominger space forms, we prove that a compact Hermitian surface with pointwise constant holomorphic sectional curvature with respect to a Gauduchon connection $\nabla^t $ is either K\"ahler,…

We show that there exist smooth, simply connected, four-dimensional spin manifolds which do not admit Einstein metrics, but nonetheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy…

We study the interplay between the following types of special non-K\"ahler Hermitian metrics on compact complex manifolds: it locally conformally K\"ahler, $k$-Gauduchon, balanced and locally conformally balanced and prove that a locally…

The Hopf surfaces provide a family of minimal non-K\"ahler surfaces of class VII on which little is known about the Chern-Ricci flow. We use a construction of Gauduchon-Ornea for locally conformally K\"ahler metrics on primary Hopf surfaces…

This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational…

We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperhermitian and para-hyperk\"ahler are analogs of the…