In this paper we have provided the " Missing Link " between κ-Minkowski spacetime and Doubly Special Relativity (DSR). We have constructed a relativistic point particle Lagrangian that has the κ-Minkowski algebra as its symplectic structure and has the DSR dispersion relation as its energy spectrum. Thus a dynamical connection between κ-Minkowski spacetime and DSR framework has been established...

In the first part of this paper [6], a method to determine Frenet apparatus of the space-like curves in Minkowski space-time is presented. In this work, the mentioned method is developed for the time-like curves in Minkowski space-time. Additionally, an example of presented method is illustrated. Keywords—Frenet Apparatus, Time-like Curves, Minkowski Space-time.

In this paper we study the geometry of Minkowski plane and obtain some results. We focus on the curve theory in Minkowski plane and prove that the total curvature of any simple closed curve equals to the total Landsberg angle. As the result, the sum of oriented exterior Landsberg angles of any polygon is also equal to the total Landsberg angle, and when the Minkowski plane is reversible, the su...

We prove a complete set of integral geometric formulas of Crofton type (involving integrations over affine Grassmannians) for the Minkowski tensors of convex bodies. Minkowski tensors are the natural tensor valued valuations generalizing the intrinsic volumes (or Minkowski functionals) of convex bodies. By Hadwiger’s general integral geometric theorem, the Crofton formulas yield also kinematic ...

In a recent paper with J. A. Wieacker it was shown that certain integral-geometric formulas of Crofton type for lower-dimensional areas carry over from Euclidean to Minkowski spaces, if the Holmes-Thompson notion of Minkowskian area is employed and the Minkowski spaces are of a special type, called hyperme-tric. Here we show rst that there exist Minkowski spaces for which, among all axiomatical...

General offset curves are treated in the context of Minkowski geometry, the geometry of the two-dimensional plane, stemming from the consideration of a strictly convex, centrally symmetric given curve as its unit circle. Minkowski geometry permits us to move beyond classical confines and provides us with a framework in which to generalize the notion of Pythagorean-hodograph curves in the case o...

5 Minkowski, R., Paris Symposium on Radio Astronomy, ed. R. N. Bracewell (Stanford: Stanford University Press, 1959), p. 315. 6 Oort, J. H., M. N., 106, 159 (1946); Problems of Cosmical Aerodynamics (Dayton: Central Air Documents Office, 1951), p. 118. 7 Baade, W., and R. Minkowski, Observatory, 74, 130 (1954). 8 Baade, W., and R. Minkowski, Ap. J., 119,206 (1954). 9Jennison, R. C., Paris Sympo...

Prompted by the development of algorithms for analysing geometric tolerancing, this article describes a method to determine the Minkowski sum for 3-dimension polytopes. This purposed method is based exclusively on intersection operations on normal cones, using the properties of the normal fan of a Minkowski sum obtained by common refinement of the normal fans of the operands. It can be used to ...

Zonotopes are becoming an increasingly popular set representation for formal verification techniques. This is mainly due to their efficient representation and their favorable computational complexity of important operations in high-dimensional spaces. In particular, zonotopes are closed under Minkowski addition and linear maps, which can be very efficiently implemented. Unfortunately, zonotopes...

A geometric algebra of point sets in the complex plane is proposed, based on two fundamental operations: Minkowski sums and products. Although the (vector) Minkowski sum is widely known, the Minkowski product of two-dimensional sets (induced by the multiplication rule for complex numbers) has not previously attracted much attention. Many interesting applications, interpretations, and connection...