On curvilinear congruences
C. E. Weatherburn · Transactions of the American Mathematical Society · 1929
In a recent paper On congruences of curves^ the writer has shown how the theory of such congruences in ordinary space of three dimensions may be extended along the lines followed for rectilinear congruences, making use of oblique curvilinear coordinates.The present paper contains a further extension of the theory, but is mainly independent of the preceding investigation.The subject is approached from a slightly different point of view, with the aid of the differential invariants grad, div, rot for three dimensions and, as far as possible, the use of coordinates is avoided.Some of the theorems proved have hitherto been known only for rectilinear congruences, while others again lose their significance in the particular case in which the lines are straight.