Summary: Considering the geometry of triply orthogonal spatial curves of congruences \(C^ 3\) in Euclidean space \(E^ 3\) related to the vortexline triad defined in an anholonomic space various kinematic and kinetic properties of viscous, compressible steady flows are examined. Beltrami and complex-lamellar vorticity vector fields are studied and it is proved that the vortexlines can be geodesics or asymptotic lines on Beltrami surfaces.