Abstract
A surface of dimension n. or n-surface. in ℝn +1 is a non-empty subset S of ℝn +1 of the form S = f−l(c) where f: U → ℝ, U open in ℝn +1 is a smooth function with the properly that ∇f(p) ≠ 0 for all p ∈ S. A 1-surfacc in ℝ2 is also called a plane curve. A 2-surface in ℝ3 is usually called simply a surface. An n-surface in ℝn +1 is often called a hypersurface. especially when n > 2.
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). 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_4
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_4
Publisher Name: Springer, New York, NY
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