Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin; Svetlana K. Zubkova

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 1, page 111-120
  • ISSN: 0231-9721

Abstract

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The second order transverse bundle T 2 M of a foliated manifold M carries a natural structure of a smooth manifold over the algebra 𝔻 2 of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general 𝔻 2 -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a 𝔻 2 -smooth foliated diffeomorphism between two second order transverse bundles maps the lift of a foliated linear connection into the lift of a foliated linear connection.

How to cite

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Shurygin, Vadim V., and Zubkova, Svetlana K.. "Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.1 (2016): 111-120. <http://eudml.org/doc/286719>.

@article{Shurygin2016,
abstract = {The second order transverse bundle $T^2_\{\}M$ of a foliated manifold $M$ carries a natural structure of a smooth manifold over the algebra $\mathbb \{D\}^2$ of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general $\mathbb \{D\}^2$-smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a $\mathbb \{D\}^2$-smooth foliated diffeomorphism between two second order transverse bundles maps the lift of a foliated linear connection into the lift of a foliated linear connection.},
author = {Shurygin, Vadim V., Zubkova, Svetlana K.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Foliation; transverse bundle; second order transverse bundle; projectable linear connection; Lie derivative; Weil bundle},
language = {eng},
number = {1},
pages = {111-120},
publisher = {Palacký University Olomouc},
title = {Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles},
url = {http://eudml.org/doc/286719},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Shurygin, Vadim V.
AU - Zubkova, Svetlana K.
TI - Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 1
SP - 111
EP - 120
AB - The second order transverse bundle $T^2_{}M$ of a foliated manifold $M$ carries a natural structure of a smooth manifold over the algebra $\mathbb {D}^2$ of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general $\mathbb {D}^2$-smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a $\mathbb {D}^2$-smooth foliated diffeomorphism between two second order transverse bundles maps the lift of a foliated linear connection into the lift of a foliated linear connection.
LA - eng
KW - Foliation; transverse bundle; second order transverse bundle; projectable linear connection; Lie derivative; Weil bundle
UR - http://eudml.org/doc/286719
ER -

References

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