Manifolds

Gerardo F. Torres del Castillo ()
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Gerardo F. Torres del Castillo: Universidad Autónoma de Puebla, Instituto de Ciencias

Chapter Chapter 1 in Differentiable Manifolds, 2012, pp 1-28 from Springer

Abstract: Abstract The basic objective of the theory of differentiable manifolds is to extend the application of the concepts and results of the calculus of the ℝ n spaces to sets that do not possess the structure of a normed vector space. The differentiability of a function of ℝ n to ℝ m means that around each interior point of its domain the function can be approximated by a linear transformation, but this requires the notions of linearity and distance, which are not present in an arbitrary set.

Keywords: Vector Field; Tensor Product; Vector Bundle; Tangent Space; Tangent Vector (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-0-8176-8271-2_1

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