For a curve on the plane, there exists at fixed distance (except for some degenerate cases). The can be alternatively produced as an envelope of circles with radius moving along . As result, when this structure is translated to three-dimensional space two parallel curves are obtained. In study defining time-like 3-dimensional Minkowski space, important theorems about these stated and proved.

Abstract. We consider some aspects of the geometry of surfaces of revolution in three-dimensional Minkowski space. First, we show that Clairaut’s theorem, which gives a well-known characterization of geodesics on a surface of revolution in Euclidean space, has an analogous result in three-dimensional Minkowski space. We then illustrate the significant differences between the two cases which ari...

This note presents elementary geometric descriptions of several simple families of harmonic functions on the upper sheet of the unit hyperboloid in Minkowski three-space. As is briefly discussed here, these calculations grew out of an earlier attempt to construct Poincaré series on punctured surfaces using Minkowski geometry. Introduction The material in this note grew out of an attempt (discus...

We show that every Lie algebra or superLie algebra has a canonical braiding on it, and that in terms of this its enveloping algebra appears as a flat space with braided-commuting coordinate functions. This also gives a new point of view about q-Minkowski space which arises in a similar way as the enveloping algebra of the braided Lie algebra gl2,q. Our point of view fixes the signature of the m...

We define new energy momentum surface density and quasilocal mass for the boundary surface of a spacelike region in spacetime. Iso-metric embeddings of such a surface into the Minkowski space are used as reference surfaces in the definition. When the reference surface lies in a flat three-dimensional space slice of the Minkowski space, our expression recovers the Brown-York and Liu-Yau quasiloc...

I. Ever since Minkowski published his four-dimensional representation of space-time, the dominant view in physics and philosophy has been that time is a fourth dimension such that human perception of change and the passage of time is a mere illusion, due to our particular slicing of space-time. But fourdimensional space-time is a block universe. This conclusion takes the form of an inference fr...