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

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

2009-06-02

arxiv.org/abs/0906.0560v3

SIGMA 5 (2009), 094, 21 pages

Mathematics

Differential Geometry

v2: an inaccuracy in constructions after formula (4.12) on page 13 (formula (51) in v1) is corrected. v3: published version

Scientific paper

10.3842/SIGMA.2009.094

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.

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