Gf-structure motivate the mathematical space

The purpose of the present paper, we have studied GF-structure motivate the mathematical space of circle in one dimensional manifolds. A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be more complicated. In the present paper, we have discussed the manifolds, the idea of dimension is important. For example lines are one dimensional, and planes two dimensional. In a one dimensional manifold, every point has a neighborhood that looks like a segment of a line. Examples of one manifold include a line, a circle and two separate circles. In a two manifold, every point has neighborhood that looks like a disk. Examples include a plane, the surface of a sphere, and the surface of tours. The trivial example of an n- dimensional manifold is . It is assumed that, in section one contains a brief introduction to GF-Structure of mathematical manifold and modeling of GF-structure manifold, while in section two, defines the special quadratic F-structure and proves some theorems. In section three, we have defined the mathematical modeling in one or more dimensional manifold. In section four, we discussed the motivational examples of manifold and construct the figures. In section five, we obtains the geometrical projection and define the slope of the geometrical equations with point (1, 0) and (-1, 0). In section six, we calculated the Nijenhuis tensor with GF-structure and proved some theorems .In the end; we are discussion the important role of mathematical space.