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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Transformations of semiholonomic 2- and 3-jets and semiholonomic prolongation of connections; pp. 375–380

(Full article in PDF format)   doi: 10.3176/proc.2010.4.18


Authors

Petr Vašík

Abstract

We recall the description of natural transformations of semiholonomic jet functors Jr defined on the categories Mfm x Mf and FMm,n. Up to order three, exact coordinate formulae are known, for general order several related results are reminded. We also show an application of semiholonomic jet transformations to prolongation of general connections.

Keywords

jet, natural transformation, connection, Ehresmann prolongation.

References

  1. Atanasiu , Gh. , Balan , V. , Brinzei , N. , and Rahula , M. Differential-Geometric Structures: Tangent Bundles , Connections in Bundles and the Exponential Law in Jet-Spaces. LKI , Moscow , 2010 (in Russian).

  2. Atanasiu , Gh. , Balan , V. , Brinzei , N. , and Rahula , M. The Differential Geometry of Second Order and Applications: The Miron–Atanasiu Theory. LKI , Moscow , 2010 (in Russian).

  3. Doupovec , M. and Mikulski , W. M. Holonomic extension of connections and symmetrization of jets. Rep. Math. Phys. , 2007 , 60(2) , 299–316.
doi:10.1016/S0034-4877(07)80141-8

  4. Kolář , I. On the torsion of spaces with connections. Czechoslovak Math. J. , 1971 , 21 , 124–136.

  5. Kolář , I. and Modugno , M. Natural maps on the iterated jet prolongation of a fibered manifold. Ann. Mat. , 1991 , CLVIII , 151–165.

  6. Kolář , I. and Vosmanská , G. Natural operations with second order jets. Rendiconti Circolo Mat. Palermo , Suppl. , Ser. II , 1987 , 14 , 179–186.

  7. Kolář , I. , Michor , P. W. , and Slovák , J. Natural Operations in Differential Geometry. Springer-Verlag , 1993.

  8. Modugno , M. Jet involution and prolongation of connections. Čas. pĕst. mat. , 1989 , 114 , 356–365.

  9. Pradines , J. Fibrés vectoriels doubles symetriques et jets holonomes d’ ordre 2. C. R. Acad. Sci. Paris , Sıer. A , 1974 , 278 , 1557–1560.

10. Vašík , P. On the Ehresmann Prolongation. Ann. Univ. Mariae Curie Sklodowska , 2007 , LXI , A , 145–153.

11. Virsik , G. On the holonomity of higher order connections. Cahiers Topol. Géom. Diff. , 1971 , 12 , 197–212.

12. Vosmanská , G. Natural transformations of semi-holonomic 3-jets. Arch. Math. , 1995 , 4 , 313–318.
 
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Current Issue: Vol. 63, Issue 4, 2014




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
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