We collect the recent results on invariant f -structures in the generalized Hermitian geometry. Here the canonical f -structures on homogeneous k-symmetric spaces play a remarkable role. Specifically, these structures provide a wealth of invariant examples for the classes of nearly Kähler f -structures, Hermitian f -structures and some others. Finally, we consider all invariant f structures on ...

We describe and construct here pseudo-Hermitian structures θ without torsion (i.e. with transversal symmetry) whose Webster-Ricci curvature tensor is a constant multiple of the exterior differential dθ. We call these structures pseudo-Hermitian Einstein and our result states that they all can be derived locally from Kähler-Einstein metrics. Moreover, we discuss the corresponding Fefferman metri...

Gray & Hervella gave a classification of almost Hermitian structures (g, I) into 16 classes. We systematically study the interaction between these classes when one has an almost hyper-Hermitian structure (g, I, J,K). In general dimension we find at most 167 different almost hyper-Hermitian structures. In particular, we obtain a number of relations that give hyperKäher or locally conformal hyper...

for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...

We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skewsymmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexion. This is naturally described by means of an extension of the notion of Killi...

We review the theory of quaternionic Kähler and hyperkähler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and with its well estabilished canonical complex structure. With an extra almost Hermitian structure on M it is possible to find a quaternionic Hermitian structure on TM , which is quaternionic Kähler if, and only if, D ...

The generalized Kähler structures were introduced and studied by M. Gualtieri in his PhD thesis [16] in the more general context of generalized geometry started by N. Hitchin in [20]. There are many explicit constructions of non-trivial generalized-Kähler structures [1, 2, 21, 24, 25, 4, 7]. For instance Gualtieri proved that all compact-even dimensional semisimple Lie groups are generalized Kä...