On Tanaka's Prolongation Procedure for Filtered Structures of Constant Type

TL;DR

This paper revisits Tanaka's prolongation procedure for filtered structures of constant type, providing a clearer and more accessible explanation aligned with Singer-Sternberg's approach, and simplifies the original complex methodology.

Contribution

The paper offers a transparent reinterpretation of Tanaka's prolongation method, making it more accessible and easier to understand compared to the original complex presentation.

Findings

Simplified presentation of Tanaka's prolongation procedure.

Clarification of the relation to Singer-Sternberg's approach.

Enhanced understanding of 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.