Differential Geometry

Abstract

The terms xij, i, j = 1, 2 can be represented as a linear combination of tangential and normal component. Each of the vectors xij can be represented as a combination of the tangent component (which itself is a combination of vectors x1 and x2) and the normal component (which is a multiple of the unit normal vector n). Let Γij and Γ 2 ij denote the coefficients of the tangent component and Lij denote the coefficient with n of vector xij. Thus,