A pair of directions emanating from a point on a surface such that the straight lines containing them are conjugate diameters of the Dupin indicatrix of at . In order that the directions , at a point on be conjugate, it is necessary and sufficient that the following condition holds
where , and are the coefficients of the second fundamental form of evaluated at . Example: a principal direction.
|||A.V. Pogorelov, "Differential geometry" , Noordhoff (1959) (Translated from Russian)|
|[a1]||W. Blaschke, K. Leichtweiss, "Elementare Differentialgeometrie" , 1 , Springer (1973)|
|[a2]||C.C. Hsiung, "A first course in differential geometry" , Wiley (1981) pp. Chapt. 3, Sect. 4|
Conjugate directions. E.V. Shikin (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Conjugate_directions&oldid=11253