View source for Conjugate net

A net of lines on a surface consisting of two families of lines such that at every point of the surface the lines from the two families of the net have [[Conjugate directions|conjugate directions]]. If a coordinate net is a conjugate net, then the coefficient <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c025/c025060/c0250601.png" /> of the second fundamental form of the surface is identically equal to zero. In a neighbourhood of every point of the surface which is not a flat point one can introduce a parametrization such that the coordinate lines form a conjugate net. One family can be chosen arbitrarily, even when the lines of this family do not have asymptotic directions. An important example is a net of lines of curvature.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.V. Pogorelov,   "Differential geometry" , Noordhoff  (1959)  (Translated from Russian)</TD></TR></table>



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  C.C. Hsiung,   "A first course in differential geometry" , Wiley  (1981)  pp. Chapt. 3, Sect. 4</TD></TR></table>