The notion of a quaternionic gerbe is presented as a new way of bundling algebraic structures over a four manifold. The structure groupoid of this fibration is described in some detail. The Euclidean conformal group RSO(4) appears naturally as a (non-commutative) monoidal structure on this groupoid. Using this monoidal structure we indicate the existence of a canonical quaternionic gerbe associ...

We discuss the Schur complement formula for quaternionic matrices, M , and give an efficient method to calculate the matrix inverse. We also introduce the functional D[M ] which extends to quaternionic matrices the non-negative number |det[M ]|. 1. Introduction. Much of the spectral theory of complex matrices does not extend to quaternion matrices without further modifications [1, 2, 3]. In par...

Nearly-quaternionic KK ahler manifolds of dimension at least 8 are shown to be quaternionic KK ahler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic KK ahler are also found.

A Riemannian manifold satis es the axiom of 2-planes if at each point, there are su ciently many totally geodesic surfaces passing through that point. Real hypersurfaces in quaternionic space forms admit nice families of tangent planes, namely, totally real, half-quaternionic and quaternionic. Several de nitions of axiom of planes arise naturally when we consider such families of tangent planes...

The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding real matrix equations is established. Keywords...

We characterise, in the setting of the Kodaira–Spencer deformation theory, the twistor spaces of (co-)CR quaternionic manifolds. As an application, we prove that, locally, the leaf space of any nowhere zero quaternionic vector field on a quaternionic manifold is endowed with a natural co-CR quaternionic structure. Also, for any positive integers k and l, with kl even, we obtain the geometric ob...

We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyse possible quaternionic groups for GUTs.

Nearly-quaternionic KK ahler manifolds of dimension at least 8 are shown to be quaternionic KK ahler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic KK ahler are also found.

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 contact manifolds. We prove that the product of the real line with a seven dimensional manifold, equipped with a certain qc structure, has a quaternionic Kähler me...

This is a continuation of a series of papers [FL1, FL2, FL3], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we continue to study the quaternionic analogues of Cauchy’s formula for the second order pole. These quaternionic analogues are closely related to regularization of infinities of vacuum ...