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...

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaterni...

Let V = R be the pseudo-Euclidean vector space of signature (p, q), p ≥ 3 and W a module over the even Clifford algebra Cl0(V ). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V )-equivariant linear map Π : ∧2W → V . If the skew symmetric vector valued bilinear form Π is nondegenerate then (M,Q) is endowed with a canonical pseudo-Riemannian metric g such that (M,Q, g) is ...

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi–centrality and centrality assumptions are also analyzed in generator terms, and implica...

A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn is presented. In particular new examples of Sp(n)Sp(1)-invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables developed by the author in two previous papers [5] and [6].

A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn is presented. In particular new examples of Sp(n)Sp(1)-invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables developed by the author in two previous papers [5] and [6].

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension of Z/2 by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.

We reformulate Special Relativity by a quaternionic algebra on reals. Using real linear quaternions, we show that previous difficulties, concerning the appropriate transformations on the 3 + 1 space-time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity. a) e-mail: [email protected]