TOPICS
Search

Third Fundamental Form


Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. Then the third fundamental form is given by

 III(v_(p),w_(p))=S(v_(p))·S(w_(p)),

where S is the shape operator.


See also

First Fundamental Form, Fundamental Forms, Second Fundamental Form, Shape Operator

Explore with Wolfram|Alpha

References

Gray, A. "The Three Fundamental Forms." §16.6 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 380-382, 1997.

Referenced on Wolfram|Alpha

Third Fundamental Form

Cite this as:

Weisstein, Eric W. "Third Fundamental Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ThirdFundamentalForm.html

Subject classifications