We prove several results on the structure of solvable quotients of fundamental groups of compact Kähler manifolds (Kähler groups).

The base space of an algebraically completely integrable Hamiltonian system acquires a rather special differential-geometric structure which plays an important role in modern physical theories such as Seiberg-Witten theory. This structure was formalised by D. Freed [1] as a Special Kähler manifold. In that paper he conjectured that there are no compact special Kähler manifolds other than flat o...

We study the interplay between following types of special non-Kähler Hermitian metrics on compact complex manifolds (locally conformally Kähler, k-Gauduchon, balanced, and locally balanced) prove that a Kähler nilmanifold carrying balanced or left-invariant k-Gauduchon metric is necessarily torus. Combined with main result in [FV16], this leads to fact 2-step endowed whichever two metrics—balan...

We construct a compact 6-dimensional solvmanifold endowed with a non-trivial generalized Kähler structure and which does not admit any Kähler metric.

In this paper we apply the hyper-Kähler quotient construction to Lie groups with a left invariant hyper-Kähler structure under the action of a closed abelian subgroup by left multiplication. This is motivated by the fact that some known hyper-Kähler metrics can be recovered in this way by considering different Lie group structures on Hp× H (H: the quaternions). We obtain new complete hyper-Kähl...

Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kähler manifolds are considered. Some necessary and sufficient conditions the investigated manifolds be isotropic hyper-Kählerian and flat are found. It is proved that the quaternionic Kähler manifolds with the considered metric structure are Einstein for dimension at least 8. The c...

The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kähler manifold. As a consequence we obtain several results on the structure of Kähler groups, i.e., the fundamental groups of compact Kähler manifolds.

In this article, we consider the almost Hermitian structure on TM induced by a pair of a metric and an affine connection on M . We find the conditions under which TM admits almost Kähler structures, Kähler structures and Einstein metrics, respectively. Moreover, we give two examples of Kähler-Einstein structures on TM . 2000 Mathematics Subject Classification: 53C55, 53C15, 53C25.

in this paper‎, ‎the‎ ‎authors prove that a strictly kähler-berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ kähler manifold‎.

We know that the existence of Kähler structure on a compact complex manifold imposes certain homological or even homotopical restrictions on its underlining topological manifold. Hodge theory is of central importance in this line. There have been recently certain extensions and progresses in this area of research. Among them is the field of Kähler groups, in which the main subject to study is t...