Some Aspects of Fundamental Forms of Surfaces and Their Interpretation

This is the authors' abstract. We don't add key points for this paper.

In this paper, we study the first and second fundamental forms of surfaces, exploring their properties as they relate to measuring arc lengths and areas, and identifying isometric surfaces. These forms can be used to define the Gaussian curvature, which is, unlike the first and second fundamental forms, independent of the parametrization of the surfaces. Also, we investigate the geometric behaviour of rectifying curves on regular surfaces under conformal and isometric transformation by using the concept of fundamental forms of surfaces.