When n is even, orthogonal spreads in an orthogonal vector space of type O-(2n 2,2) are used to construct line-sets of size (2nm1 + 1)2”-’ in W2”~’ all of whose angles are 90” or cos -1(2-(“-2)/2). These line-sets are then used to obtain quatemionic Kerdock Codes. These constructions are based on ideas used by Calderbank, Cameron, Kantor, and Seidel in real and complex spaces.

The study of surfaces in threeand higher-dimensional spaces has seen a resurgence of interest recently due to various applications of these surfaces to various areas of mathematical physics, especially to the area of integrable systems [1, 6, 8]. The particular class of surfaces known as minimal surfaces with constant mean curvature has many applications to various physical problems. It is the ...

We show that for all very special quaternionic manifolds a different N = 1 reduction exists, defining a Kähler Geometry which is “dual” to the original very special Kähler geometry with metric Gab̄ = −∂a∂b lnV (V = 1 6dabcλaλbλc). The dual metric g = V (G) is Kähler and it also defines a flat potential as the original metric. Such geometries and some of their extensions find applications in Type...

From the classical differential equation of Jacobi fields, one naturally defines the Jacobi operator of a Riemannian manifold with respect to any tangent vector. A straightforward computation shows that any real, complex and quaternionic space forms satisfy that any two Jacobi operators commute. In this way, we classify the real hypersurfaces in quaternionic projective spaces all of whose tange...

In classical case there is simplest method of error correction with using three equal bits instead of one. In the paper is shown, how the scheme fails for quantum error correction with complex vector spaces of usual quantum mechanics, but works in real and quaternionic cases. It is discussed also, how to implement the three qubits scheme with using encoding of quaternionic qubit by Majorana spi...

In this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real Brauer-Severi varieties, under the action of the Galois group Gal(C/R). Appropriate stabilizations of these spaces yield two equivariant spectra. The first one classifies Dupont/Seymour’s quaternionic K-theory, and the other one classifies and equivariant cohomology theory Z∗(−) which is a natural recip...

We provide a general criteria for the integrability of the almost para-quaternionic structure of an almost para-quaternionic manifold (M,P) of dimension 4m ≥ 8 in terms of the integrability of two or three sections of the defining rank three vector bundle P. We relate it with the integrability of the canonical almost complex structure of the twistor space and with the integrability of the canon...

Spaces in the genus of infinite quaternionic projective space which admit essential maps from infinite complex projective space are classified. In these cases the sets of homotopy classes of maps are described explicitly. These results strengthen the classical theorem of McGibbon and Rector on maximal torus admissibility for spaces in the genus of infinite quaternionic projective space. An inte...