# Weingarten derivational formulas

From Encyclopedia of Mathematics

Formulas yielding the expansion of the derivative of the unit normal vector to a surface in terms of the first derivatives of the position vector of this surface. Let be the position vector of the surface, let be the unit normal vector and let , , , , , be the coefficients of the first and second fundamental forms of the surface, respectively; the Weingarten derivational formulas will then take the form

The formulas were established in 1861 by J. Weingarten.

#### References

[1] | P.K. Rashevskii, "A course of differential geometry" , Moscow (1956) (In Russian) |

#### Comments

#### References

[a1] | W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie" , Springer (1973) |

[a2] | N.J. Hicks, "Notes on differential geometry" , v. Nostrand (1965) |

**How to Cite This Entry:**

Weingarten derivational formulas. A.B. Ivanov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Weingarten_derivational_formulas&oldid=13541

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098