Equi-conjugate pair of curves in a hypersurface of En+1

Equi-conjugate pair of curves in a Euclidean hypersurface V _n is defined and it is shown that such a pair is characterised by the relation _n ² =k _k l sin² _kl. Furthermore, it is proved that the expression , evaluated for n mutually equi-conjugate directions at a point P of V _n , is independent of these n directions and therefore is an invariant for V _n .