CONSTRUCTION OF NONCOMMUTATIVE INSTANTONS IN 4k DIMENSIONS

We consider generalized self-duality equations for U (2r) Yang–Mills theory on ℝ4k with quaternionic structure and self-dual Moyal deformation. We employ the extended ADHM method in 4k dimensions to construct new noncommutative generalizations of the 't Hooft as well as of the BPST instantons. It is shown that in the commutative limit the BPST-type configurations coincide with the standard instantons on ℍPk written in local coordinates.

An example of rank two symmetric Osserman space

Recently, Blažić, Bokan and Rakić, obtained some classes of 4-dimensional Osserman pseudo-Riemannian manifolds. One of these is the class of rank 2 locally symmetric space endowed with an integrable para-quaternionic structure. In this paper we give an explicit construction of an example of a space of that kind.

Quaternionic Transformations of a Non-Positive Quaternionic Kähler Manifold

Let (M,g,Q) be a simply connected, complete, quaternionic Kähler manifold without flat de Rham factor. Then any 1-parameter group of transformations of M which preserve the quaternionic structure Q preserves also the metric g. Moreover, if (M,g) is irreducible then the quaternionic Kähler metric g on (M,Q) is unique up to a homothety.