Abstract A capacitance in physics is calculated by integration on a compact collection in R^3 This cincept was represented by Wiener and Loewner in 1924 and then expanded to R^n space by Foerstman, Poussin and some other french Mathematicians. Ferrand declared the concept of Riemannian manifolds in R^n . In this thesis, we study all the says of Ferrand during mentioned years which are presented in a seminar. These concepts also are entered in Finsler spaces and some of cases are proved on Finsler manifolds. At the last part of thesis we try to develop related cases of action of conformal transformations group on the Riemann to Finsler space.

The purpose of this research is to test the effect of new technology on the improvement of learning of geometry (2) -the circle section- of the grade 3 of high school. Fifty male students were selected from a southwestern city of Iran, Khoraamshahr and divided two homogeneous groups in control and experimental. The students of both groups are evaluated a researcher-made test at the end of the study. the geometrical issues were taught by means of new technology to the experimental group while the control group received Traditional teaching method. The results indicate that the experimental group outperformed the control group in solving the geometrical problems. Furthermore, the experimental group performed better on the comprehension of circle-related concepts. In addition, the experimental group used more strategies in solving the geometrical problems than the control group

In this thesis, we study Finsler metrics of scalar flag curvature. We find that a non-Riemannian quantity is closely related to the flag curvature. We show that this non-Riemannian quantity takes a special form if and only if the flag curvature takes a special form. This will lead to a better understanding on Finsler metrics of scalar flag curvature.