On tanaka's prolongation procedure for filtered structures of constant type

Abstract

We present Tanaka's prolongation procedure for filtered structures on manifolds discovered in [Tanaka N., J. Math. Kyoto. Univ. 10 (1970),1-82] in a spirit of Singer- Sternberg's description of the prolongation of usual G-structures [Singer I.M., Sternberg S., J. Analyse Math. 15 (1965),1-114; Sternberg S., Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964]. This approach gives a transparent point of view on the Tanaka constructions avoiding many technicalities of the original Tanaka paper.