Abstract
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.
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Sobczyk, G. (2013). Differential Geometry of k-Surfaces. In: New Foundations in Mathematics. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8385-6_15
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