【作者】 何勇；

【导师】 王宝勤；

【作者基本信息】 新疆师范大学 ， 基础数学， 2005， 硕士

【摘要】 本文用纤维丛理论给出了Finsler空间子流形上的两种诱导联络的定义,这两种定义不必依赖于度量张量,不涉及Finsler空间与其子流形上Finsler函数之间复杂的诱导关系,仅使用一般的“诱导张量”,这两种诱导联络形式具体、简明。本文分为三部分:第一部分为预备知识,给出了基本概念、定义及定理。Finsler联络可用联络形式ωba和基形(θv)a( a ,b= 1n,n=dim M )来确定。第二部分从这种形式的联络入手,以Finsler张量场的投影为诱导张量对ωba和(θv)a中的联络系数协变分量下降指标,得出新的联络系数协变分量,从而诱导出Finsler空间子流形上的Finsler联络。若取度量张量为诱导联络,则又给出了由Cartan联络给出的诱导联络。第三部分给出了Finsler空间子流形上的诱导无挠联络。这部分首先给出了导出坐标系下Finsler空间无挠联络的表达式,然后指出P*T M上(r,s)型Chern-Finsler张量场集合与P *TM1上同型张量场集合之间可建立一个模同态,称为投影,最后,以Chern-Finsler张量场的投影为诱导张量,给出了Finsler空间子流形的诱导无挠联络。更多还原

【Abstract】 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更多还原