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...

This paper introduces a no vel quaternion{valued MLP{ type net w ork called the Quaternionic Spinor MLP (QSMLP). In con trast to another recently proposed Quaternionic MLP it uses spinors in its propagation function. This allows very eÆciently the processing of 3D vector data, whic his demonstrated by experiments. The QSMLP is pro ven to be a universal approximator and a learning algorithm for ...

We present a novel full-rate full-diversity orthogonal space-time block code for QPSK modulation and 4 transmit antennas based on quaternionic algebra. The code does not result in constellation expansion unlike other full-rate full-diversity codes in the literature. The quaternionic structure of the code is exploited to reduce the complexity of maximum likelihood (ML) coherent decoding from a s...

The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by inhomogeneous Dirac and Schrödinger equations. Mixing of hyper-complex components of wavefunctions occurs through their interaction with potentials dissipative into ...

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...

Colour image representation using real quaternions has shown to be very useful for linear and morphological colour filtering. This paper deals with the extension of first derivatives-based structure tensor for various quaternionic colour image representations. Classical corner and edge features are obtained from eigenvalues of the quaternionic colour structure tensors. We study the properties o...

By considering the three-dimensional incompressible Euler equations, a 4-vector ζ is constructed out of a combination of scalar and vector products of the vorticity ω and the vortex stretching vector ω · ∇u = Sω. The evolution equation for ζ can then be cast naturally into a quaternionic Riccati equation. This is easily transformed into a quaternionic zero-eigenvalue Schrödinger equation whose ...

A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in [11]. Several results of the theory recall the classical complex analysis, whereas other results reflect the peculiarity of the quaternionic structure. The recent [1] identified a larger class of domains, on which the study of regular functions is most natural and not limited to t...