Darboux trihedron

A trihedron associated with a point on a surface and defined by a triple of vectors, given by the normal unit vector to the surface and two mutually orthogonal principal unit tangent vectors and to the surface such that

The properties of the surface can be described in terms of displacement of the Darboux trihedron when its base point describes the surface. A systematic use of the Darboux trihedron in the study of surfaces led G. Darboux [1] to the moving-frame method.

References

[1]	G. Darboux, "Leçons sur la théorie générale des surfaces et ses applications géométriques du calcul infinitésimal" , 1 , Gauthier-Villars (1887)

Comments

A Darboux trihedron is also called a Darboux frame. It is also introduced in affine differential geometry, cf. [a1].

References

[a1]	H.W. Guggenheimer, "Differential geometry" , McGraw-Hill (1963)