Darboux frame
（重定向自Geodesic torsion）
![A Darboux trihedron consisting of a point P and three orthonormal vectors e1, e2, e3 based at P.](/Images/godic/202501/15/Darboux_trihedron.svg0121.png")
In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame as applied to surface geometry. A Darboux frame exists at any non-umbilic point of a surface embedded in Euclidean space. It is named after French mathematician Jean Gaston Darboux.