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  JP Journal of Geometry and Topology  
 ISSN: 0972-415X
 
 
 

     JP Journal of Geometry and Topology
    Volume 7, Issue 2, Pages 271 - 282 (July 2007)


A FAMILY OF GOURSAT SYSTEMS AND THEIR ABNORMAL CURVES

M. Cheaito (Lebanon) and M. Mehdi (Lebanon)

Received October 11, 2006; Revised March 28, 2007.

References:



[1] R. Bryant and L. Hsu, Rigidity of integral curves of rank two distributions, Vent. Math. 114 (1993), 435-461.

[2] E. Cartan, Les systèmes de Pfaff à cinq variables et les équations aux dérivées partielles du second ordre, Ann. Ec. Norm. XXVII(3) (1910), 109-192.

[3] M. Cheaito and P. Mormul, Rank-2 distributions satisfying the Goursat conditions: all their local models in dimensions 7 and 8, ESAIM: Control, Optimisation and Calculus of Variations, 1999.

[4] F. Engel, Zurinvariantentheorie der Systems von Pfaff’schen Gleichungen, Leipzig Berichte, Math. Phys. 41 (1889), 157-176.

[5] A. Kumpera and C. Ruiz, Sur l’équivalence locale des systèmes de Pfaff en drapeau, In: Monge-Ampère Equations and Related Topics, Inst. Alta. Math., Rome 1982,201-248.

[6] W. Liu and H. J. Sussmann, Shortest paths for sub-Riemannian metrics of rank-two distributions, Mem. Amer. Math. Soc. 118 (1995), 564.

[7] R. Montgomery, A survey of singular curves in sub–Riemannian geometry, J. Dynam. Control Systems 1 (1995), 49-90.

[8] P. Mormul, Local Models of 2-Distributions in 5 Dimensions Everywhere Fulfilling the Goursat Condition, Séminaire Rouen, 1994.

[9] M. Zhitomirskii, Normal forms of germs of distributions with a fixed segment of growth vector (traduction anglaise), Leningrad Math. J. 2 (1991), 1043-1065.

[10] M. Zhitomirskii, Rigid and abnormal normal line subdistributions of 2-distributions, J. Dynam. Control Systems 1(2) (1995), 253-294.

Keywords and phrases: Pfaffian systems, vector distributions, abnormal curve.

Communicated by Yasuo Matsushita

 


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