Differential Geometry of k-Surfaces

  • Garret Sobczyk


We have discussed the calculus of a k-surface, or a k-manifold \(\mathcal{M}\) embedded in \({\mathbb{R}}^{n}\) in  Chap. 13, utilizing the basic building block of a k-rectangle. In differential geometry, a k-surface is rigorously defined by an atlas of charts which maps the points of open sets in \({\mathbb{R}}^{k}\) onto regions in the manifold \(\mathcal{M}\) in a one-to-one continuous and differentiable manner, in much the same way that the maps of an atlas represent the surface of the Earth.


Tangent Space Tangent Vector Unit Normal Vector Shape Operator Geometric Algebra 
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Authors and Affiliations

  • Garret Sobczyk
    • 1
  1. 1.Departamento de Física y MatemáticasUniversidad de Las AméricasPueblaMexico

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