Special tangent valued forms and the Frölicher-Nijenhuis bracket

Antonella Cabras; Ivan Kolář

Archivum Mathematicum (1993)

  • Volume: 029, Issue: 1-2, page 71-82
  • ISSN: 0044-8753

Abstract

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We define the tangent valued C -forms for a large class of differential geometric categories. We deduce that the Frölicher-Nijenhuis bracket of two tangent valued C -forms is a C -form as well. Then we discuss several concrete cases and we outline the relations to the theory of special connections.

How to cite

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Cabras, Antonella, and Kolář, Ivan. "Special tangent valued forms and the Frölicher-Nijenhuis bracket." Archivum Mathematicum 029.1-2 (1993): 71-82. <http://eudml.org/doc/247446>.

@article{Cabras1993,
abstract = {We define the tangent valued $C$-forms for a large class of differential geometric categories. We deduce that the Frölicher-Nijenhuis bracket of two tangent valued $C$-forms is a $C$-form as well. Then we discuss several concrete cases and we outline the relations to the theory of special connections.},
author = {Cabras, Antonella, Kolář, Ivan},
journal = {Archivum Mathematicum},
keywords = {category over manifolds; tangent valued form; Frölicher-Nijenhuis bracket; special connections; connections; tangent valued -forms; Frölicher-Nijenhuis bracket},
language = {eng},
number = {1-2},
pages = {71-82},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Special tangent valued forms and the Frölicher-Nijenhuis bracket},
url = {http://eudml.org/doc/247446},
volume = {029},
year = {1993},
}

TY - JOUR
AU - Cabras, Antonella
AU - Kolář, Ivan
TI - Special tangent valued forms and the Frölicher-Nijenhuis bracket
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 1-2
SP - 71
EP - 82
AB - We define the tangent valued $C$-forms for a large class of differential geometric categories. We deduce that the Frölicher-Nijenhuis bracket of two tangent valued $C$-forms is a $C$-form as well. Then we discuss several concrete cases and we outline the relations to the theory of special connections.
LA - eng
KW - category over manifolds; tangent valued form; Frölicher-Nijenhuis bracket; special connections; connections; tangent valued -forms; Frölicher-Nijenhuis bracket
UR - http://eudml.org/doc/247446
ER -

References

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  2. The System of Principal Connections, Rendiconti di Mat., Ser VII, Roma 11 (1991), 849-871. (1991) MR1151603
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  6. Natural Operations in Differential Geometry, Springer - Verlag, 1993. (1993) MR1202431
  7. On the algebraic structure of the bundles of higher velocities, Seminari Instituto di Mat. Appl. “G. Sansone”, Florence (1989), 17 pp. (1989) 
  8. On the algebraic structure on the jet prolongations of fibred manifolds, Czechoslovak Math. J. 40 (1990), 601-611. (1990) MR1084896
  9. Remarks on the Frölicher-Nijenhuis bracket, Diff. Geom. and Its Applications, Proc. Conf. J.E. Purkyně University, Brno (1987), 197-220. (1987) Zbl0633.53024MR0923350
  10. Systems of vector valued forms on a fibred manifold and applications to gauge theories, Proc. Conf. Diff. Geom. Math. in Math. Phys., Salamanca 1985, Lect. Not. Math. 1251, Springer, 1987, 238-264. Zbl0614.53072MR0897122

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