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Title: Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles (English)
Author: Shurygin, Vadim V.
Author: Zubkova, Svetlana K.
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 55
Issue: 1
Year: 2016
Pages: 111-120
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: Foliation
Keyword: transverse bundle
Keyword: second order transverse bundle
Keyword: projectable linear connection
Keyword: Lie derivative
Keyword: Weil bundle
MSC: 53C12
MSC: 53C15
MSC: 58A20
MSC: 58A32
idZBL: Zbl 1365.58003
idMR: MR3674605
Date available: 2016-08-30T12:02:23Z
Last updated: 2018-01-10
Stable URL:
Reference: [1] Evtushik, L. E., Lumiste, Yu. G., Ostianu, N. M., Shirokov, A. P.: Differential-geometric structures on manifolds.. In: Problemy Geometrii. Itogi Nauki i Tekhniki 9, VINITI Akad. Nauk SSSR, Moscow, 1979, 5–246. Zbl 0455.58002, MR 0573267
Reference: [2] Gainullin, F. R., Shurygin, V. V.: Holomorphic tensor fields and linear connections on a second order tangent bundle.. Uchen. Zapiski Kazan. Univ. Ser. Fiz.-matem. Nauki 151, 1 (2009), 36–50. Zbl 1216.53019
Reference: [3] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry.. Springer, Berlin, 1993. MR 1202431
Reference: [4] Molino, P.: Riemannian Foliations.. Birkhäuser, Boston, 1988. Zbl 0824.53028, MR 0932463
Reference: [5] Morimoto, A.: Prolongation of connections to tangent bundles of higher order.. Nagoya Math. J. 40 (1970), 99–120. MR 0279719, 10.1017/S002776300001388X
Reference: [6] Morimoto, A.: Prolongation of connections to bundles of infinitely near points.. J. Different. Geom. 11, 4 (1976), 479–498. Zbl 0358.53013, MR 0445422, 10.4310/jdg/1214433720
Reference: [7] Pogoda, Z.: Horizontal lifts and foliations.. Rend. Circ. Mat. Palermo 38, 2, suppl. no. 21 (1989), 279–289. Zbl 0678.57013, MR 1009580
Reference: [8] Shurygin, V. V.: Structure of smooth mappings over Weil algebras and the category of manifolds over algebras.. Lobachevskii J. Math. 5 (1999), 29–55. Zbl 0985.58001, MR 1752307
Reference: [9] Shurygin, V. V.: Smooth manifolds over local algebras and Weil Bundles.. J. Math. Sci. 108, 2 (2002), 249–294. Zbl 1007.58001, MR 1887820, 10.1023/A:1012848404391
Reference: [10] Shurygin, V. V.: Lie jets and symmetries of geometric objects.. J. Math. Sci. 177, 5 (2011), 758–771. MR 2786527, 10.1007/s10958-011-0507-3
Reference: [11] Vishnevskii, V. V.: Integrable affinor structures and their plural interpretations.. J. Math. Sci. 108, 2 (2002), 151–187. MR 1887816, 10.1023/A:1012818202573
Reference: [12] Wolak, R.: Normal bundles of foliations of order $r$.. Demonstratio Math. 18, 4 (1985), 977–994. Zbl 0609.58004, MR 0857354


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