Abstract
We have finally arrived at the subject of surfaces. This topic is extraordinarily rich and it lets tensor calculus shine at its brightest. We will focus on two-dimensional surfaces in three-dimensional Euclidean spaces. The Euclidean space in which the surface is embedded is called the ambient space. The analysis presented in this chapter is easily extended to hypersurfaces of any dimension. A hypersurface is a differentiable (n − 1)-dimensional subspace of an n-dimensional space. That is, a hypersurface is characterized by a codimension of 1, codimension being the difference between the dimensions of the ambient and embedded spaces. Curves, the subject of Chap. 13, embedded in the three-dimensional Euclidean space have codimension two.
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Grinfeld, P. (2013). The Tensor Description of Embedded Surfaces. In: Introduction to Tensor Analysis and the Calculus of Moving Surfaces. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7867-6_10
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