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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 094, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.094 (Mi sigma440) 		 
This article is cited in 20 scientific papers (total in 20 papers)

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
Full-text PDF (321 kB) Citations (20)
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DOI: https://doi.org/10.3842/SIGMA.2009.094
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.
Keywords: $G$-structures; filtered structures; generalized Spencer operator; prolongations.
Received: June 2, 2009; in final form September 29, 2009; Published online October 6, 2009
Bibliographic databases:
Document Type: Article
MSC: 58A30; 58A17
Language: English
Citation: Igor Zelenko, “On Tanaka's Prolongation Procedure for Filtered Structures of Constant Type”, SIGMA, 5 (2009), 094, 21 pp.
Citation in format AMSBIB
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    		Symmetry, Integrability and Geometry: Methods and Applications
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