Natural operations on holomorphic forms

A. Navarro; J. Navarro; C. Tejero Prieto

Archivum Mathematicum (2018)

  • Volume: 054, Issue: 4, page 239-254
  • ISSN: 0044-8753

Abstract

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We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence à la Galois.

How to cite

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Navarro, A., Navarro, J., and Tejero Prieto, C.. "Natural operations on holomorphic forms." Archivum Mathematicum 054.4 (2018): 239-254. <http://eudml.org/doc/294155>.

@article{Navarro2018,
abstract = {We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence à la Galois.},
author = {Navarro, A., Navarro, J., Tejero Prieto, C.},
journal = {Archivum Mathematicum},
keywords = {natural bundles; natural operations},
language = {eng},
number = {4},
pages = {239-254},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Natural operations on holomorphic forms},
url = {http://eudml.org/doc/294155},
volume = {054},
year = {2018},
}

TY - JOUR
AU - Navarro, A.
AU - Navarro, J.
AU - Tejero Prieto, C.
TI - Natural operations on holomorphic forms
JO - Archivum Mathematicum
PY - 2018
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 054
IS - 4
SP - 239
EP - 254
AB - We prove that the only natural differential operations between holomorphic forms on a complex manifold are those obtained using linear combinations, the exterior product and the exterior differential. In order to accomplish this task we first develop the basics of the theory of natural holomorphic bundles over a fixed manifold, making explicit its Galoisian structure by proving a categorical equivalence à la Galois.
LA - eng
KW - natural bundles; natural operations
UR - http://eudml.org/doc/294155
ER -

References

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  13. Navarro, J., Sancho, J.B., 10.1016/j.difgeo.2014.12.003, Differential Geom. Appl. 38 (2015), 159–174. (2015) MR3304675DOI10.1016/j.difgeo.2014.12.003
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