Search results for "Unit tangent vector"

Integration on Surfaces

2012

We intend to study the integration of a differential k-form over a regular k-surface of class C 1 in \(\mathbb{R}^n\). To begin with, in Sect. 7.1, we undertake the integration over a portion of the surface that is contained in a coordinate neighborhood. Where possible, we will express the obtained results in terms of integration of vector fields. For example, we study the integral of a vector field on a portion of a regular surface in \(\mathbb{R}^3\) and also the integral over a portion of a hypersurface in \(\mathbb{R}^n\). In Sect. 7.3 we study the integration of differential k-forms on regular k-surfaces admitting a finite atlas.We discuss the need for the surface to be orientable so t…