On Harmonic Theory in Flows

[摘要] Recently [8], a harmonic theory was developed for a compactcontact manifold from the viewpoint of the transversal geometry ofcontact flow. A contact flow is a typical example of geodesibleflow. As a natural generalization of the contact flow, the presentpaper develops a harmonic theory for various flows on compactmanifolds. We introduce the notions of $H$-harmonic and$H^*$-harmonic spaces associated to a H"ormander flow. We alsointroduce the notions of basic harmonic spaces associated to a weakbasic flow. One of our main results is to show that in the specialcase of isometric flow these harmonic spaces are isomorphic to thecohomology spaces of certain complexes. Moreover, we find anobstruction for a geodesible flow to be isometric.

[学科分类] 数学（综合）

[关键词] contact structure;geodesible flow;isometric flow;basic cohomology