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Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin; Svetlana K. Zubkova — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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...

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