# The vertical prolongation of the projectable connections

Annales UMCS, Mathematica (2012)

- Volume: 66, Issue: 1, page 1-5
- ISSN: 2083-7402

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topAnna Bednarska. "The vertical prolongation of the projectable connections." Annales UMCS, Mathematica 66.1 (2012): 1-5. <http://eudml.org/doc/267710>.

@article{AnnaBednarska2012,

abstract = {We prove that any first order F2 Mm1,m2,n1,n2-natural operator transforming projectable general connections on an (m1,m2, n1, n2)-dimensional fibred-fibred manifold p = (p, p) : (pY : Y → Y) → (pM : M → M) into general connections on the vertical prolongation V Y → M of p: Y → M is the restriction of the (rather well-known) vertical prolongation operator V lifting general connections Γ on a fibred manifold Y → M into VΓ (the vertical prolongation of Γ) on V Y → M.},

author = {Anna Bednarska},

journal = {Annales UMCS, Mathematica},

keywords = {Fibred-fibred manifold; natural operator; projectable connection; fibred-fibred manifold; vertical prolongation},

language = {eng},

number = {1},

pages = {1-5},

title = {The vertical prolongation of the projectable connections},

url = {http://eudml.org/doc/267710},

volume = {66},

year = {2012},

}

TY - JOUR

AU - Anna Bednarska

TI - The vertical prolongation of the projectable connections

JO - Annales UMCS, Mathematica

PY - 2012

VL - 66

IS - 1

SP - 1

EP - 5

AB - We prove that any first order F2 Mm1,m2,n1,n2-natural operator transforming projectable general connections on an (m1,m2, n1, n2)-dimensional fibred-fibred manifold p = (p, p) : (pY : Y → Y) → (pM : M → M) into general connections on the vertical prolongation V Y → M of p: Y → M is the restriction of the (rather well-known) vertical prolongation operator V lifting general connections Γ on a fibred manifold Y → M into VΓ (the vertical prolongation of Γ) on V Y → M.

LA - eng

KW - Fibred-fibred manifold; natural operator; projectable connection; fibred-fibred manifold; vertical prolongation

UR - http://eudml.org/doc/267710

ER -

## References

top- Doupovec, M., Mikulski, W. M., On the existence of prolongation of connections, Czechoslovak Math. J., 56 (2006), 1323-1334. Zbl1164.58300
- Kolář, I., Connections on fibered squares, Ann. Univ. Mariae Curie-Skłodowska Sect. A 59 (2005), 67-76.
- Kolář, I., Michor, P. W. and Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993. Zbl0782.53013
- Kolář, I., Mikulski, W. M., Natural lifting of connections to vertical bundles, The Proceedings of the 19th Winter School "Geometry and Physics" (Srní, 1999). Rend. Circ. Mat. Palermo (2) Suppl. No. 63 (2000), 97-102. Zbl0978.53056
- Kurek, J., Mikulski, W. M., On prolongations of projectable connections, Ann. Polon. Math, 101 (2011), no. 3, 237-250. Zbl1230.58007
- Mikulski, W. M., The jet prolongations of fibered-fibered manifolds and the flow operator, Publ. Math. Debrecen 59 (2001), no. 3-4, 441-458. Zbl0996.58002
- Kolář, I., Some natural operations with connections, J. Nat. Acad. Math. India 5 (1987), no. 2, 127-141. Zbl0671.53023

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