We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k − 1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic whose isometry group c...

We define an (equivariant) quaternionic analytic torsion for antiselfdual vector bundles on quaternionic Kähler manifolds, using ideas by Leung and Yi. We compute this torsion for vector bundles on quaternionic homogeneous spaces with respect to any isometry in the component of the identity, in terms of roots and Weyl groups. 2000 Mathematics Subject Classification: 53C25, 58J52, 53C26, 53C35

We show that, if a quaternionic k-dimensional vector bundle l' over the quaternionic projective space Hpn is stably extendible and its non-zero top Pontrjagin class is not zero mod 2, then l' is stably equivalent to the Whitney sum of k quaternionic line bundles provided k S; n.

We study the quaternionic linear system which is composed out of terms of the form ln(x) := ∑n p=1 apxbp with quaternionic constants ap, bp and a variable number n of terms. In the first place we investigate one equation in one variable. If n = 2 the corresponding equation, which is normally called Sylvester’s equation will be treated completely by using only quaternionic algebra. For larger n ...

The pseudo-Riemannian manifold M = (M, g), n ≥ 2 is paraquaternionic Kähler if hol(M) ⊂ sp(n,R)⊕sp(1, R). If hol(M) ⊂ sp(n, R), than the manifold M is called para-hyperKähler. The other possible definitions of these manifolds use certain parallel para-quaternionic structures in End(TM), similarly to the quaternionic case. In order to relate these different definitions we study para-quaternionic...

The research reported in this paper is motivated by the study of stability for linear dynamical systems with quaternionic coefficients. These systems can be used to model several physical phenomena, for instance, in areas such as robotics and quantum mechanics. More concretely, quaternions are a powerful tool in the description of rotations [1]. There are situations, especially in robotics, whe...

The paper compares the features of three extensions of the notion of the Gabor’s analytic signal for 2-D signals: the analytic signals with single-quadrant spectra (AS), the quaternionic signals with quaternionic single-quadrant spectra (QS) and the monogenic signals (MS). A good platform of comparison are the polar representations of the AS and the QS and the spherical coordinate representatio...

We construct N = 2 superspace Lagrangians for quaternionic symmetric σmodels G/H × Sp(1), or equivalently, quaternionic potentials for these symmetric spaces. They are homogeneous H invariant polynomials of order 4 which are similar to the quadratic Casimir operator of H. The construction is based on an identity for the structure constants specific for quaternionic symmetric spaces. † On leave ...

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CHn, n ≥ 3. For the quaternionic hyperbolic spaces HHn, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificat...

In this paper we investigate statistical manifolds with almost quaternionic structures. We define the concept of quaternionic Kähler-like statistical manifold and derive the main properties of quaternionic Kähler-like statistical submersions, extending in a new setting some previous results obtained by K. Takano concerning statistical manifolds endowed with almost complex and almost contact str...