Geodesic
Natural differential operators between some natural bundles
Mathematica Bohemica, Tome 118 (1993) no. 2, pp. 153-161

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/MB.1993.126052
Classification : 53A55, 58A20
Keywords: natural bundles; natural differential operators 
Mikulski, W. M. Natural differential operators between some natural bundles. Mathematica Bohemica, Tome 118 (1993) no. 2, pp. 153-161. doi: 10.21136/MB.1993.126052
@article{10_21136_MB_1993_126052,
     author = {Mikulski, W. M.},
     title = {Natural differential operators between some natural bundles},
     journal = {Mathematica Bohemica},
     pages = {153--161},
     year = {1993},
     volume = {118},
     number = {2},
     doi = {10.21136/MB.1993.126052},
     mrnumber = {1223480},
     zbl = {0777.58004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.126052/}
}
TY  - JOUR
AU  - Mikulski, W. M.
TI  - Natural differential operators between some natural bundles
JO  - Mathematica Bohemica
PY  - 1993
SP  - 153
EP  - 161
VL  - 118
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.126052/
DO  - 10.21136/MB.1993.126052
LA  - en
ID  - 10_21136_MB_1993_126052
ER  - 
%0 Journal Article
%A Mikulski, W. M.
%T Natural differential operators between some natural bundles
%J Mathematica Bohemica
%D 1993
%P 153-161
%V 118
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.126052/
%R 10.21136/MB.1993.126052
%G en
%F 10_21136_MB_1993_126052

[1] J. Dębecki: Natural transformations of afinors into functions and afìnors. Supplemento ai Rendiconti del Circolo Matematico di Palermo (1991), in press.

[2] D. B. A. Epstein: Natural tensors on Riemmannian manifolds. Ј. Differential Geometry, 631-645. | MR

[3] D. B. A. Epstein W.P. Thurston: Transformation groups and natural bundles. Proc. London Math. Soc. (3) 38 (1979), 219-236. | MR

[4] J. Gancarzewicz: Differential Geometry. B.M.64, 1987. (In Polish.) | MR

[5] J. Gancarzewicz: Liftings of functions and vector fields to natural bundles. Dissertationes Mathematicae, Warszawa (1982). | MR | Zbl

[6] T. Klein: Connection on higher order tangent bundles. Čas. Pӗst. Mat. 106 (1981), 414-424. | MR

[7] I. Kolář: Functorial prolongations of Lie groups and their actions. Čas. Pěst. Mat. 108 (1983), 289-294. | MR

[8] I. Kolář J. Slovák: On the geometric functors on manifolds. Suplemento ai Rendiconti del Circolo Matematico di Palermo (1988), 223-233. | MR

[9] W. M. Mikulski: Continuity of liftings. Čas. Pěst. Mat. 113 (4) (1988), 359-362. | MR | Zbl

[10] A. Morimoto: Prolongations of connections to bundles of infinitely near points. Ј. Differential Geometry 11 (1976), 479-498. | DOI | MR

[11] A. Nijenhuis: Natural bundles and their general properties. Differential Geometry, Kinokuniya, Тokio (1972), 317-343. | MR | Zbl

[12] R. S. Palais C. L. Terng: Natural bundles have finite order. Тopology 16 (1977), 271-277. | MR

[13] J. Slovák: On the finite ordeг of some operators. Proc. of the Conf., Brno, 1986.

[14] A. Zajtz: Foundation of differential geometry on natural bundles. Caracas, 1984, preprint.

Cité par Sources :