On the nets of equi-conjugate pairs of curves in a Weyl hypersurface (Q1580992)

The authors study a hypersurface \(W_n\) in an \((n+1)\)-dimensional Weyl space \(W_{n+1}\). They define the equiconjugate pair of curves on \(W_n\): curves of such a pair are conjugate, and the normal curvatures in their directions are equal. They also determine a relation connecting the above common normal curvature, the sectional curvatures, and the angle between the directions of such curves. Finally, they investigate special nets (Chebyshev of two kinds and geodesic) formed by the tangent vector fields of equiconjugate pairs of curves.