Ida Cristian, Oană Alexandru
Department of Mathematics and Computer Science, Transilvania University of Braşov, Street Iuliu Maniu 50, 500091 Braşov, Romania.
ScientificWorldJournal. 2015;2015:218912. doi: 10.1155/2015/218912. Epub 2015 Mar 5.
We consider the lift of a foliation to its conormal bundle and some transverse geometrical structures associated with this foliation are studied. We introduce a good vertical connection on the conormal bundle and, moreover, if the conormal bundle is endowed with a transversal Cartan metric, we obtain that the lifted foliation to its conormal bundle is a Riemannian one. Also, some transversally framed f(3, ε)-structures of corank 2 on the normal bundle of lifted foliation to its conormal bundle are introduced and an almost (para)contact structure on a transverse Liouville distribution is obtained.
我们考虑叶状结构到其余法丛的提升，并研究与该叶状结构相关的一些横向几何结构。我们在余法丛上引入一个良好的垂直联络，此外，如果余法丛赋予一个横向嘉当度量，我们得到提升到其余法丛的叶状结构是一个黎曼叶状结构。而且，我们引入了提升到其余法丛的叶状结构的法丛上余秩为2的一些横向框架f(3, ε)-结构，并在一个横向刘维尔分布上得到一个几乎（仿）接触结构。
