Two Types Of Induced Connections On The Submanifold In A Finsler Space

In this paper, the author gives two types of definitions for the induced connection on the submanifold in a Finsler space by the concept of fiber bundle,the definitions need not depend on the metric tensor and merely uses a general"inducing tensor",and do not involve the complex induced relations between the Finsler function on the Finsler space and it's submanifold . The expression of these induced connections are particular , simple and wise.The paper is divided into three sections: the first section is some basic concept,definitions and theorems.Finsler connection can be determined by connection formω_b^a and base form (θ^v)^a( a ,b= 1…n,n=dim M). In the second section, begin with this kind of form of Finsler connection, we take the projection of Finsler tensor field as induced tensor, make the index of covariant component of coefficient of connection inω_b^a and (θ^v)^a be fallen , then ,we gain to new covariant component of coefficient of connection, so we induced the Finsler connection on Finsler submanifold in Finsler space. If the metric tensor is taken as induced tensor, the induced connection obtained from Cartan connection is given.In the third section, the definition of torsion free connection is given . first of all, the expression for torsion free connection on Finsler submanifold in Finsler space is given under induced coordinate system, second ,it is pointed out that a modular homorphism can be established between (r,s) Chern-Finsler tensor field on P^*TM and P^*TM₁, it is called projection ,at last ,the projection of Chern-Finsler...