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

2013/01/22 by Cristian Ida, Ida, Cristian, Adelina Manea +1
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Ophthalmology and Eye Disorders #math.DG

paper · pdf · doi:10.48550/arxiv.1301.5316

arXiv admin note: substantial text overlap with arXiv:1301.5275; and text overlap with arXiv:1003.2518, arXiv:1004.0796, arXiv:1202.6202 by other authors. Accepted for publication in IJGMMP 2014

arxiv created 2014/01/22 · arxiv updated 2014/01/23

Abstract

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 Vrănceanu 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^*M₀ given by vertical foliation F_V and the line foliation F_C^* 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_V_C^* and the natural almost complex structure on T^*M₀ we study some aspects concerning the cohomology of c--indicatrix cotangent bundle.

Citations

• Adapted basic connections to a certain subfoliation on the tangent manifold of a Finsler space
• A Kähler Structure on Cartan Spaces
• Looking for Kähler- Einstein Structure on Cartan Spaces with Berwald connection
• Selected papers

Related

• Vertical Liouville foliations on the big-tangent manifold of a Finsler space
• Adapted basic connections to a certain subfoliation on the tangent manifold of a Finsler space
• Liouville structures
• Liouville-type theorems for foliations with complex leaves
• Harmonic functions on R-covered foliations and group actions on the circle