Related papers: Invariant pseudo Kaehler metrics in dimension four

We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat…

We construct the normal forms of null-K\"ahler metrics: pseudo-Riemannian metrics admitting a compatible parallel nilpotent endomorphism of the tangent bundle. Such metrics are examples of non-Riemannian holonomy reduction, and (in the…

A Riemannian manifold $(M,\rho)$ is called Einstein if the metric $\rho$ satisfies the condition $\Ric (\rho)=c\cdot \rho$ for some constant $c$. This paper is devoted to the investigation of $G$-invariant Einstein metrics with additional…

We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…

Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are bi-Lagrangian and that they are obtained by complex submanifolds via…

In this paper the certain 4-dimensional algebra in 4-dimensional pseudo-Riemannian space with signature (1, -1, -1, -1) is constructed. On the basis of this algebra the elements of the analysis, i.e. the theory of 4-dimensional functions of…

We study homogeneous Einstein metrics on indecomposable non-K\"ahlerian C-spaces, i.e. even-dimensional torus bundles $M=G/H$ with $\mathsf{rank} G>\mathsf{rank} H$ over flag manifolds $F=G/K$ of a compact simple Lie group $G$. Based on the…

We construct explicit Einstein-Kahler metrics in all even dimensions D=2n+4 \ge 6, in terms of a $2n$-dimensional Einstein-Kahler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter,…

We completely characterize cosymplectic and $\alpha$-cosymplectic Lie algebras in terms of corresponding symplectic Lie algebras and suitable derivations on them. Several examples are given and classification results are obtained in…

For any Lagrangean K\"ahler submanifold $M \subset T^*{\Bbb C}^n$, there exists a canonical hyper K\"ahler metric on $T^*M$. A K\"ahler potential for this metric is given by the generalized Calabi Ansatz of the theoretical physicists…

Given a path of almost-K\"ahler metrics compatible with a fixed symplectic form on a compact 4-manifold such that at time zero the almost-K\"ahler metric is an extremal K\"ahler one, we prove, for a short time and under a certain…

We study the existence of invariant Einstein metrics on real flag manifolds associated to simple and non-compact split real forms of complex classical Lie algebras whose isotropy representation decomposes into two or three irreducible…

We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic…

Simply-connected four-dimensional gradient Ricci solitons that are invariant under a compact cohomogeneity one group action have been studied extensively. However, the special case where the group is $SU(2)$ (the smallest possible example)…

In this paper, we investigate left invariant Riemannian metrics on Lie groups with one and two-dimensional commutator subgroups. We explicitly provide the Levi-Civita connection, sectional curvature, and Ricci curvature, and we give…

We classify homogeneous pseudo-Riemannian manifolds of index 4 which admit an invariant almost hyper-Hermitian structure and an H-irreducible isotropy group. The main result is that all these spaces are flat except in dimension 12.

We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler metrics with vanishing scalar curvature which are invariant under the conformal action of Bianchi V group. The…

On a 3-manifold bounding a compact 4-manifold, let a conformal structure be induced from a complete Einstein metric which conformally compactifies to a K\"ahler metric. Formulas are derived for the eta invariant of this conformal structure…

We classify flat strict nearly K\"ahler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-K\"ahler factor of maximal dimension and a strict flat nearly K\"ahler manifold of split…

Motivated by understanding the limiting case of a certain systolic inequality we study compact Riemannian manifolds having all harmonic 1-forms of constant length. We give complete characterizations as far as K\"ahler and hyperbolic…