Abstract
In the previous chapter, we emphasized the central role of the tangent space in differential geometry. The tangent space at a point is a set whose elements, tangent vectors, arise from calculus in at least two equivalent ways. We have also seen examples of how nonlinear geometric objects can arise from an object defined pointwise at the algebraic level of the tangent spaces. For example, vector fields give rise to more global geometric objects such as integral curves and diffeomorphisms. The passage from the algebraic tangent spaces to the geometric space in these examples was a process of “integration.”
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McInerney, A. (2013). Differential Forms and Tensors. In: First Steps in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7732-7_4
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