Natural differential operators between some natural bundles

Włodzimierz M. Mikulski

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 2, page 153-161
  • ISSN: 0862-7959

Abstract

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Let F and G be two natural bundles over n -manifolds. We prove that if F is of type (I) and G is of type (II), then any natural differential operator of F into G is of order 0. We give examples of natural bundles of type (I) or of type (II). As an application of the main theorem we determine all natural differential operators between some natural bundles.

How to cite

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Mikulski, Włodzimierz M.. "Natural differential operators between some natural bundles." Mathematica Bohemica 118.2 (1993): 153-161. <http://eudml.org/doc/29206>.

@article{Mikulski1993,
abstract = {Let $F$ and $G$ be two natural bundles over $n$-manifolds. We prove that if $F$ is of type (I) and $G$ is of type (II), then any natural differential operator of $F$ into $G$ is of order 0. We give examples of natural bundles of type (I) or of type (II). As an application of the main theorem we determine all natural differential operators between some natural bundles.},
author = {Mikulski, Włodzimierz M.},
journal = {Mathematica Bohemica},
keywords = {natural bundles; natural differential operators; natural bundles; natural differential operators},
language = {eng},
number = {2},
pages = {153-161},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Natural differential operators between some natural bundles},
url = {http://eudml.org/doc/29206},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - Natural differential operators between some natural bundles
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 2
SP - 153
EP - 161
AB - Let $F$ and $G$ be two natural bundles over $n$-manifolds. We prove that if $F$ is of type (I) and $G$ is of type (II), then any natural differential operator of $F$ into $G$ is of order 0. We give examples of natural bundles of type (I) or of type (II). As an application of the main theorem we determine all natural differential operators between some natural bundles.
LA - eng
KW - natural bundles; natural differential operators; natural bundles; natural differential operators
UR - http://eudml.org/doc/29206
ER -

References

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  10. A. Morimoto, 10.4310/jdg/1214433720, Ј. Differential Geometry 11 (1976), 479-498. (1976) MR0445422DOI10.4310/jdg/1214433720
  11. A. Nijenhuis, Natural bundles and their general properties, Differential Geometry, Kinokuniya, Тokio (1972), 317-343. (1972) Zbl0246.53018MR0380862
  12. R. S. Palais C. L. Terng, Natural bundles have finite order, Тopology 16 (1977), 271-277. (1977) MR0467787
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