Abstract
Let f: U → ℝ be a smooth function, where U ⊂ ℝn +1 is an open set. let c ∈ ℝ be such that f−1(c) is non-empty, and let p ∈ f−1(c). A vector at p is said to be tangent to the level set f−1(c) if it is a velocity vector of a parametrized curve in ℝn +1 whose image is contained in f−1(c) (see Figure 3.1).
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). The Tangent Space. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_3
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6155-1
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