Prolongation of tangent valued forms to Weil bundles

Antonella Cabras; Ivan Kolář

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 2, page 139-145
  • ISSN: 0044-8753

Abstract

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We prove that the so-called complete lifting of tangent valued forms from a manifold M to an arbitrary Weil bundle over M preserves the Frölicher-Nijenhuis bracket. We also deduce that the complete lifts of connections are torsion-free in the sense of M. Modugno and the second author.

How to cite

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Cabras, Antonella, and Kolář, Ivan. "Prolongation of tangent valued forms to Weil bundles." Archivum Mathematicum 031.2 (1995): 139-145. <http://eudml.org/doc/247680>.

@article{Cabras1995,
abstract = {We prove that the so-called complete lifting of tangent valued forms from a manifold $M$ to an arbitrary Weil bundle over $M$ preserves the Frölicher-Nijenhuis bracket. We also deduce that the complete lifts of connections are torsion-free in the sense of M. Modugno and the second author.},
author = {Cabras, Antonella, Kolář, Ivan},
journal = {Archivum Mathematicum},
keywords = {Weil bundle; tangent valued form; Frölicher-Nijenhuis bracket; complete lift; connection; torsion; prolongations of tensor fields; Fröhlicher-Nijenhuis bracket; Weil bundle; Weil algebra},
language = {eng},
number = {2},
pages = {139-145},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Prolongation of tangent valued forms to Weil bundles},
url = {http://eudml.org/doc/247680},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Cabras, Antonella
AU - Kolář, Ivan
TI - Prolongation of tangent valued forms to Weil bundles
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 2
SP - 139
EP - 145
AB - We prove that the so-called complete lifting of tangent valued forms from a manifold $M$ to an arbitrary Weil bundle over $M$ preserves the Frölicher-Nijenhuis bracket. We also deduce that the complete lifts of connections are torsion-free in the sense of M. Modugno and the second author.
LA - eng
KW - Weil bundle; tangent valued form; Frölicher-Nijenhuis bracket; complete lift; connection; torsion; prolongations of tensor fields; Fröhlicher-Nijenhuis bracket; Weil bundle; Weil algebra
UR - http://eudml.org/doc/247680
ER -

References

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  1. Complete lifts of tensor fields of type ( 1 , k ) to natural bundles, Zeszyty Nauk. UJ, Krak¢w 23 (1982), 43–79. (1982) Zbl0547.55014MR0670571
  2. Lifts of some tensor fields and connections to product preserving functors, to appear in Nagoya Math. J. MR1295815
  3. Covariant approach to natural transformations of Weil functors, Comment. Math. Univ. Carolinae 27 (1986), 723–729. (1986) MR0874666
  4. Natural operations in differential geometry, Springer-Verlag 1993. MR1202431
  5. Torsions of connections on some natural bundles, Differential Geometry and Its Applications 2 (1992), 1–16. (1992) MR1244453
  6. Graded Lie algebras and connections on a fibred space, Journ. Math. Pures and Appl. 83 (1984), 111–120. (1984) MR0776913
  7. Prolongations of connections to bundles of infinitely near points, J. Diff. Geo. 11 (1976), 479–498. (1976) MR0445422
  8. Prolongations of connections and sprays with respect to Weil functors, Suppl. Rendiconti Circolo Mat. Palermo, Serie II 14 (1987), 143–155. (1987) MR0920852
  9. Théorie des pointes proches sur les variétés différentielles, Colloque de topologie et géométrie différentielle, Strasbourg (1953), 111–117. (1953) MR0061455

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