A vertical Liouville subfoliation on the cotangent bundle of a Cartan space and some related structures

作者：Ida Cristian^*; Manea Adelina

来源：International Journal of Geometric Methods in Modern Physics, 2014, 11(6): 1450063.

DOI：10.1142/S0219887814500637

• Cartan space
• foliation
• basic connection
• cohomology

In this paper, we study some problems related to a vertical Liouville distribution (called vertical Liouville-Hamilton distribution) on the cotangent bundle of a Cartan space. We study the existence of some linear connections of Vranceanu type on Cartan spaces related to some foliated structures. Also, we identify a certain (n, 2n - 1)-codimensional subfoliation (F-V, F-C*) on T*M-0 given by vertical foliation F-V and the line foliation FC* spanned by the vertical Liouville-Hamilton vector field C* and we give a triplet of basic connections adapted to this subfoliation. Finally, using the vertical Liouville foliation F-VC* and the natural almost complex structure on T*M-0 we study some aspects concerning the cohomology of c-indicatrix cotangent bundle.

• 出版日期2014-7