The Discussion About The Properties Of Pseudo-Finsler Manifold

In this paper, we discuss some main properties on pseudo- Finsler manifold. The paper is divided into five sections. It includes some basic concepts and definitions in the first section.We start the second section with the concept of associate linear connection to FC on pseudo-Finsler manifold, where FC is the Finsler connection. By means of the associate coordinate system, the connection is induced and proved as the associate linear connection to FC on the pseudo-Finsler submanifold.In the third section, the horizontal flag curvature, as the main property on pseudo-Finsler manifold, is discussed. By using the relation of canonical non-linear connection and induced non-linear connection, we present a comparison between the induced and intrinsic the horizontal flag curvature. It will play a profound role in the studying of the pseudo-Finsler geometry.In the forth section, we develop the pseudo-Finsler manifold of scalar curvature. The conditions of constant scalar curvature are obtained and proved. Furthermore, we get the condition about the constant pseudo-Finsler.The last section, the relation of curvature is presented on the projec-...