Abstract
A vector field X on an n-surface S ⊂ ℝn+1 is a function which assigns to each point p in S a vector X(p) ∈ ℝ n+1 p at p. If X(p) is tangent to S (i.e., X(p) ∈ Sp) for each p ∈ S, X is said to be a tangent vector field on S. If X(p) is orthogonal to S (i.e.. X(p) ∈ S ⊥p ) for each p ∈ S, X is said to be a normal vector field on S (see Figure 5.1).
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). Vector Fields on Surfaces; Orientation. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_5
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6155-1
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