As observed by Choi et al. (1999), curves in Minkowski space R2,1 are very well suited to describe the medial axis transform (MAT) of a planar domain, and Minkowski Pythagorean hodograph (MPH) curves correspond to domains, where both the boundaries and their offsets are rational curves (Moon, 1999). Based on these earlier results, we give a thorough discussion of G1 Hermite interpolation by MPH...

Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its va...

We give a differential geometric interpretation for the classification of biharmonic curves in semi-Euclidean 3-space due to Chen and Ishikawa (1991).

In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set {K, KII , H, HII}, where (K,H) and (KII , HII) are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.

A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski space is proposed and its properties examined. In this scheme the structure of spacetime is intrinsically quantum mechanical. It is shown that the causal ge...

When Alice went Through the Looking Glass [1], she found herself in a situation where she had to run as fast as she could in order to stay still. In accordance with the dictum that truth is stranger than fiction, we will see that it is possible to find a situation in special relativity where running towards one’s target is actually counter-productive. Although the situation is easily analysed a...

We wish to report here on a recent approach [1] to the non-commutative calculus on q-Minkowski space which is based on the reflection equations (RE) with no spectral parameter. These are considered as the expression of the invariance (under the coaction of the q-Lorentz group) of the commutation properties which define the different q-Minkowski algebras. This approach also allows us to discuss ...

By using an n–Dimensional Minkowski space, the space–time algebra is introduced. It is used for discussing physical problems of special relativity.