New Approaches on Dual Space

Abstract

In this paper, we give how to define the basic concepts of differential geometry on Dual space. For this, dual tangent vectors that have p as dual point of application are defined. Then, the dual analytic functions defined by Dimentberg are examined in detail, and by using the derivative of the these functions, dual directional derivatives and dual tangent maps are introduced.

An overview to analyticity of dual functions

“…Given the dual functions ξ : U ⊆ D n → D m , ξ = ξ 1 , ..., ξ m , we conclude that if the dual functions ξ j : U ⊆ D n → D, (1 ≤ j ≤ m) are dual analytic, then the dual function ξ is dual analytic. When the above information is taken into consideration, the following functions can be defined: [31].…”