Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 094, 21 pages      arXiv:0906.0560
Contribution to the Special Issue “Élie Cartan and Differential Geometry”

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

Igor Zelenko
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA

Received June 02, 2009, in final form September 29, 2009; Published online October 06, 2009

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.

Key words: G-structures; filtered structures; generalized Spencer operator; prolongations.

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