In this study, we study rotational hypersurfaces in 4-dimensional Lorentz-Minkowski space. We find the about spacelike axis according to Gaussian and mean curvatures $E_{1}^{4}$ give some results with aid of curvatures. After that, deal Gauss map hypersurface by obtaining obtain second third Laplace-Beltrami operators on $E_{1}^{4}$. Also, these characterizations for timelike lightlike axes, too.

We characterize all ruled translating solitons in Minkowski 3-space. In contrast to the Euclidean space, we find that are not cylindrical. These surfaces appear when vector field defines rulings, viewed as a curve, is lightlike straight line. also classify cylindrical solitons, obtaining can be considered analogous grim reapers of but other which have no counterpart space.

The samples of geometric interpretation of space-time features of special relativity theory and phyllotaxis botanic phenomenon demonstrate variance of Minkovski’s theory application in mathematic modeling of natural phenomena. It is a well-known fact that in 1908, i.e. three years after A. Einstein’s theory of relativity was published, mathematician G. Minkowski made public geometric interpreta...

The concept of range symmetric matrix is introduced in Minkowski space m. Equivalent conditions for a matrix to be range symmetric are determined. The existence of the Minkowski inverse of a range symmetric matrix in m is discussed.

Non-extreme walls (bubbles with two insides) and ultra-extreme walls (bubbles of false vacuum decay) are discussed. Their respective energy densities are higher and lower than that of the corresponding extreme (supersymmetric), planar domain wall. These singularity free space-times exhibit non-trivial causal structure analogous to certain non-extreme black holes. We focus on anti-de Sitter– Min...