We generalise the Kreck-Stolz invariants s2 and s3 by defining a new invariant, the t-invariant, for quaternionic line bundles E over closed spinmanifolds M of dimension 4k−1 with H3(M ;Q) = 0 such that c2(E) ∈ H4(M) is torsion. The t-invariant classifies closed smooth oriented 2-connected rational homology 7-spheres up to almost-diffeomorphism, that is, diffeomorphism up to a connected sum wit...

Real Nullstellensatz is a classical result from Algebraic Geometry. It has recently been extended to quaternionic polynomials by Alon and Paran [1]. The aim of this paper extend their Quaternionic matrix polynomials. We also obtain an improvement the for [4] in sense that we simplify definition real left ideal. use methods proof version Hilbert's [5] extensions mildly non-commutative case case.

The main technical result of the paper is a Bochner type formula for the sub-laplacian on a quaternionic contact manifold. With the help of this formula we establish a version of Lichnerowicz’ theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the Sp(n)Sp(1) components of the qc-Ricci curvature. It is shown that in the case of a 3-Sasakian manifold the l...

The quaternionic KP hierarchy is the integrable hierarchy of p.d.e obtained by replacing the complex numbers with the quaternions in the standard construction of the KP hierarchy and its solutions; it is equivalent to what is often called the Davey-Stewartson II hierarchy. This article studies its relationship with the theory of conformally immersed tori in the 4-sphere via quaternionic holomor...

A version of Lichnerowicz’ theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the Sp(1)Sp(1) component of the qc-Ricci curvature on a compact seven dimensional quaternionic contact manifold is established. It is shown that in the case of a seven dimensional compact 3-Sasakian manifold the lower bound is reached if and only if the quaternionic contact man...