On Calculus of Manifolds with Special Emphasis of 3D Minkowski Space M2,1

Abstract

In this paper, we explain some topics of calculus of manifold, especially for the spacetime symmetry topic. With emphasis of 3D Minkowski differential geometry. The most important symmetries are nbsp, A diffeomorphism of this symmetry is called the isometry. If a one-parameter group of isometries is generated by a vector field, then quotthis vector field is called a Killing vector field. Which shows that the Lei derivative is vanishingquot [14]. Moreover the one parameter group of diffeomorphism called the flow. However the Poincare#39 group quotis the group of isometries of Minkowski spacetime. Also quotit is a full symmetry of special relativity includes the translations , rotation and boostsquot [11]