in this work, different types of chaotic 1-manifolds which lie on the chaotic spheres or on a torus are introduced. some types of retractions of the chaotic spheres affect on the 1-chaotic systems, and other types of retractions occur to the geometric manifold but make the 1-chaotic manifold invariant. the existed retractions are discussed through new proved theorems. also we construct diffe...

This paper aims to generate materices of rotations in Minkowski using the Lie Derivative. The calculus on manifolds Lorentzian spaces are used matrices rotation three-dimensional Lorentz-Minkowski space which includes one axis timelike and other two spacelike axes. findings showed that their dramatically increased use derivative many branches mathematics physics, also revealed ( rotation) leave...

We show that Special and General Relativity lead to the introduction of an observer manifold, in addition usual event manifold. Axiomatics require manifolds be Hausdorff are not appropriate for propose alternative axiomatics how most local computations extend this framework without difficulty. The derivation Lorentz transformation takes a new meaning context, enabling identification representat...

We classify the paracontact Riemannian manifolds that their Riemannian curvature satisfies in the certain condition and we show that this classification is hold for the special cases semi-symmetric and locally symmetric spaces. Finally we study paracontact Riemannian manifolds satisfying R(X, ξ).S = 0, where S is the Ricci tensor.

Higher spin tensor gauge fields have natural gauge-invariant field equations written in terms of generalised curvatures, but these are typically of higher than second order in derivatives. We construct geometric second order field equations and actions for general higher spin boson fields, and first order ones for fermions, which are non-local but which become local on gauge-fixing, or on intro...

We study homogeneous Lorentzian manifolds M=G/L of a connected reductive Lie group G modulo subgroup L, under the assumption that M is (almost) G-effective and isotropy representation totally reducible. show description such reduces to case semisimple groups G. Moreover, we prove space reductive. describe all reducible subgroups Lorentz divide them into three types. The Type I are compact, whil...

The most thoroughly understood example of superstring compactification is compactification on a fiat torus [1]. This example is exactly soluble and obeys all of the equations of string theory. It is also clearly a significant example since it is one way to understand the construction of the heterotic string theory [2]. For compact~ficatlon of physical dimensions from ten to four, the fiat torus...

We prove the theorem valid for (Pseudo)-Riemannian manifolds V n : "Let x 2 V n be a xed point of a homothetic motion which is not an isometry then all curvature invariants vanish at x." and get the Corollary: "All curvature invariants of the plane wave metric ds 2 = 2 du dv + a 2 (u) dw 2 + b 2 (u) dz 2 identically vanish." Analysing the proof we see: The fact that for deenite signature atness...

The interest in string Hamiltonian system has recently been rekindled due to its application to target-space duality. In this article, we explore another direction it motivates. In Sec. 1, conformal symmetry and some algebraic structures of the system that are related to interacting strings are discussed. These lead one naturally to the study of Lorentz surfaces in Sec. 2. In contrast to the ca...