Differential Geometry of k-Surfaces

Garret Sobczyk
Additional contact information
Garret Sobczyk: Universidad de Las Américas, Departamento de Física y Matemáticas

Chapter Chapter 15 in New Foundations in Mathematics, 2013, pp 253-274 from Springer

Abstract: 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.

Keywords: Tangent Space; Tangent Vector; Unit Normal Vector; Shape Operator; Geometric Algebra (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8385-6_15

Ordering information: This item can be ordered from
http://www.springer.com/9780817683856

DOI: 10.1007/978-0-8176-8385-6_15

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().