The area element for a surface with first
fundamental form
is
where
is the wedge product.
See also
Area,
First Fundamental Form,
Line Element,
Riemannian
Metric,
Surface Area,
Volume
Element
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References
Gray, A. "The Intuitive Idea of Area on a Surface." §15.3 in Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, pp. 351-353, 1997.Referenced on Wolfram|Alpha
Area Element
Cite this as:
Weisstein, Eric W. "Area Element." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AreaElement.html
Subject classifications