The vertical prolongation of the projectable connections
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2012)
- Volume: 66, Issue: 1
- ISSN: 0365-1029
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topAnna Bednarska. "The vertical prolongation of the projectable connections." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 66.1 (2012): null. <http://eudml.org/doc/289820>.
@article{AnnaBednarska2012,
abstract = {We prove that any first order $\mathcal \{F\}_2\mathcal \{M\}_\{m_1,m_2,n_1,n_2\}$-natural operator transforming projectable general connections on an $(m_1,m_2, n_1, n_2)$-dimensional fibred-fibred manifold $p = (p, p) : (p_Y : Y \rightarrow Y ) \rightarrow (p_M : M \rightarrow M)$ into general connections on the vertical prolongation $V Y \rightarrow M$ of $p: Y \rightarrow M$ is the restriction of the (rather well-known) vertical prolongation operator $\mathcal \{V\}$ lifting general connections $\overline\{\Gamma \}$ on a fibred manifold $Y \rightarrow M$ into $\mathcal \{V\}\overline\{\Gamma \}$ (the vertical prolongation of $\overline\{\Gamma \}$) on $V Y \rightarrow M$.},
author = {Anna Bednarska},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Fibred-fibred manifold; natural operator; projectable connection},
language = {eng},
number = {1},
pages = {null},
title = {The vertical prolongation of the projectable connections},
url = {http://eudml.org/doc/289820},
volume = {66},
year = {2012},
}
TY - JOUR
AU - Anna Bednarska
TI - The vertical prolongation of the projectable connections
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2012
VL - 66
IS - 1
SP - null
AB - We prove that any first order $\mathcal {F}_2\mathcal {M}_{m_1,m_2,n_1,n_2}$-natural operator transforming projectable general connections on an $(m_1,m_2, n_1, n_2)$-dimensional fibred-fibred manifold $p = (p, p) : (p_Y : Y \rightarrow Y ) \rightarrow (p_M : M \rightarrow M)$ into general connections on the vertical prolongation $V Y \rightarrow M$ of $p: Y \rightarrow M$ is the restriction of the (rather well-known) vertical prolongation operator $\mathcal {V}$ lifting general connections $\overline{\Gamma }$ on a fibred manifold $Y \rightarrow M$ into $\mathcal {V}\overline{\Gamma }$ (the vertical prolongation of $\overline{\Gamma }$) on $V Y \rightarrow M$.
LA - eng
KW - Fibred-fibred manifold; natural operator; projectable connection
UR - http://eudml.org/doc/289820
ER -
References
top- Doupovec, M., Mikulski, W. M., On the existence of prolongation of connections, Czechoslovak Math. J., 56 (2006), 1323-1334.
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- Kolar, I., Michor, P. W. and Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
- Kolar, I., Mikulski, W. M., Natural lifting of connections to vertical bundles, The Proceedings of the 19th Winter School “Geometry and Physics” (Srn´ı, 1999). Rend.
- Circ. Mat. Palermo (2) Suppl. No. 63 (2000), 97-102.
- Kurek, J., Mikulski, W. M., On prolongations of projectable connections, Ann. Polon. Math, 101 (2011), no. 3, 237-250.
- Mikulski, W. M., The jet prolongations of fibered-fibered manifolds and the flow operator, Publ. Math. Debrecen 59 (2001), no. 3-4, 441-458.
- Kolar, I., Some natural operations with connections, J. Nat. Acad. Math. India 5 (1987), no. 2, 127-141.
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