TYPES OF 3D SURFACE OF ROTATIONS EMBEDDED IN 4D MINKOWSKI SPACE

Abstract

The geometry of surfaces of rotation in three dimensional Euclidean spaces has been studied widely. The rotational surfaces in three dimensional Euclidean spaces are generated byrotating an arbitrary curve about an arbitrary axis. Which should be using a type of matrices called matrices of rotation. But they are should be created by one parameter group of isometry. On the other hand, the Minkowski spaces have shorter history. In 1908 Minkowski [1864-1909] gave his talk on four dimensional real vector space, with a symmetric form of signature (+,+,+,-).  In this space there are different types of vectors/ axes (space-liketime- like and null) as well as different types of curves (space-like- time-like and null). The relationship between Euclidean and Minkowskian geometry has many intriguing aspects, one of which is the manner in which formal similarity can co-exist with significantgeometric disparity. There has been considerable interest in the comparison of these twogeometries, as can be seen in the lecture notes of L’opez. In this manuscript we produce different types of surfaces of rotation in four dimensionalMinkowski spaces. And then we will provide a brief description of surfaces of rotation of 4D Minkowski spaces. Firstly consider the beginning by creating different type of matrices of rotation corresponding to the appropriate subgroup of the Lorentz group, and then generate all types of surfaces of rotation. The new work here is the spherical symmetric case which is nonabeliansubalgebra isomorphic to lie algebra. This case is known by expectation.