Abstracto
- In differential geometry the curves and surfaces in R3 are usually studied employing the vector formalism. In the case of a differentiable curve, at each point a triad of mutually orthogonal unit vectors (called tangent, normal and binormal) is constructed and the rates of change of these vectors along the curve define the curvature and torsion of the curve. These two functions characterize the curve completely except for its position and orientation in space. In a simi lar manner, at each point of a smooth surface a triad of mutually orthogonal unit vectors can be defined in such a way that one of these vectors is normal to the surface. Then the rate of variation of the normal unit vector to the surface along the directions of the other two vectors determines the curvature of the surface