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adjoint complex affine geometry arbitrary asymptotic curves asymptotic surface C-congruence C-surface Ch-correlation Christoffel symbols components conformal connection conic conjugate contact of order covariant covariant derivative curvature tensor curve defined Definition denote derivatives determined elemental congruence elemental surfaces equations 9 equations hold f-invariant focal envelope focal planes focal points following theorem four-dimensional functions g-angle Gaussian curvature given line Hence intersection invariant K-line K-plane K-points K-quadric Kabcd line space linear complex linear congruence linearly independent matrix metric geometry metric tensor necessary and sufficient numbers obtain order at least parabolic congruence parameter pencil polar plane preceding theorem principal CC-surface Problem projective angle projectively orthogonal proof follows proof is similar prove quadric rank regulus Remark respect ruled surface ruling satisfies the equation scalar second osculating K-space solution sufficient condition surface p(t tangent plane teleparallel tensor abc Theorem 9 theorem follows transformation law unit complex vanish vector