Interpolating trajectories of points and geometric entities is an important problem for kinematics. To describe these trajectories, several algorithms have been proposed using matrices, quaternions, dual-quaternions, the Study quadric; last one allows embedding motors as 8D vectors into projective space P7, where interpolation rotations translations becomes a linear problem. Furthermore, confor...

The properties of spinors and vectors in (2 + 2) space split quaternions are studied. Quaternionic representation rotations naturally separates two SO(2,1) subgroups the full group symmetry norms quaternions, SO(2,2). One them represents symmetries three-dimensional Minkowski space-time. Then, second subgroup, generated by additional time-like coordinate from basis can be viewed as internal mod...

The research on this paper started with an attempt to understand the geometry of Bennett linkages [1–6] from the point of view of dual quaternions. The group of Euclidean displacements can be embedded as an open subset of the Study quadric in the projectivization of the dual quaternions regarded as a real vector space of dimension eight. Rotation subgroups and and their composition then get an ...

We give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples with a fully homogeneous action of a semisimple Lie group, and to construct distinct para-quaternio...