【作者】 王旭升；

【导师】 陈群；

【作者基本信息】 武汉大学 ， 基础数学， 2017， 硕士

【摘要】 在这篇文章中,我们设n维流形M具有黎曼度量g和正交联络▽,且引用Cartan关于正交联络的一些结论来做一些工作。在第一章中,我们介绍E.Cartan工作,即他把正交联络的挠率张量分解为三个部分,然后引入我们的工作。在第二章中,我们介绍一些基础知识。在第三章中,我们推导正交联络下的基本方程,并给出其在正交标架场下的表达式。在第四章中,我们在具有正交联络的3维流形下讨论,并假设这个流形的挠率张量A是全反对称的。得到与Levi-civita联络下截面曲率和常截面曲率的全脐子流形类似的结果。更多还原

【Abstract】 In this paper,we give an n-dimensional manifold M equipped with some Riemanni-an metric g and orthogonal connections ▽.We invoke Cartan’s results about orthogonal connection to do some work.In the first chapter,we introduce Cartan’s work,that is the orthogornal connection can be split into three components,then induce our new work.In the second chapter,we introduce some basic knowledge.In the third chapter,we calculate the fundamental equations under orthogonal connection,and then obtain the expression under orthonormal frame field.In the last chapter,we begin our discussion in 3-dimensional manifold equipped with orthogonal connection.And we also assume the torsion tensor A is totally anti-symmetric.we obtain the results about sectional curvatures and totally umbilical sub-manifold of constant sectional curvature,which are similar with that under Levi-civita connection.更多还原