Abstract
Let S be an n-surfacc in ℝn +1, oriented by the unit normal vcctor field N, and let p ∈ S. The Weingarten map L p : S p → S p , defined by L p (v) = − ∇v N for v ∈ S p , measures the turning of the normal as one moves in S through p with various velocities v. Thus L p measures the way S curves in ℝn +1 at p. For n = 1, we have seen that L p is just multiplication by a number K(p) the curvature of S at p. We shall now analyze L p when n > 1.
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). Curvature of Surfaces. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_12
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6155-1
Online ISBN: 978-1-4612-6153-7
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