The conformal infinity of a quaternionic-Kähler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n− 1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be the...

The conformal infinity of a quaternionic-Kähler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n − 1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be th...

In this paper, we introduce a new processing procedure for quaternionic signals through consideration of the well-known orthogonal matching pursuit (OMP), which provides sparse approximation. Due to quaternions noncommutativity, two quaternionic extensions are presented: the right-multiplication quaternionic OMP, that can be used to process right-multiplication linear combinations of quaternion...

We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non–commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and ordinary symplectic structure. \pacs{} Typeset using REVTEX 1 Recently, one of us (SLA) has proposed a generalization of Heisenberg picture quantum mechanics, termed gen...

It is shown that all but at most countably many spaces in the genus of HP∞, the infinite quaternionic projective space, do not admit any essential maps from CP∞, the infinite complex projective space. This strengthens a theorem of McGibbon and Rector which states that among the uncountably many homotopy types in its genus, HP∞ is the only one which admits a maximal torus.

In this paper, we determine the total Stiefel-Whitney classes of vector bundles over the product of the complex projective space CP (j) with the quaternionic projective space HP (k). Moreover, we show that every involution fixing CP (2m+1)×HP (k) bounds. AMS subject classifications: 57R85, 57S17, 55N22

In this article, quaternionic curves in 3-dimensional Euclidean space have examined. Firstly, algebraic properties of quaternions and their basic definitions theorems are given. Later, some characterizations the Mannheim obtained.

In the space H of quaternions, we investigate a natural, invariant geometry of the open, unit disc ∆H and of the open half-space H . These two domains are diffeomorphic via a Cayley-type transformation. We first study the geometrical structure of the groups of Möbius transformations of ∆H and H + and identify original ways of representing them in terms of two (isomorphic) groups of matrices wit...