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高校应用数学学报
高校应用数学学报  2014, Vol. 29 Issue (3): 319-332    
    
扩展的Bianchi恒等式及其在几何流演化方程中的应用
赵春莉1, 卢卫君2
1. 浙江大学 数学中心, 浙江杭州 310027
2. 广西民族大学 理学院, 广西南宁 530006
The extended Bianchi identities and their applications in evolution equations along the geometric flows
ZHAO Chun-li1, LU Wei-jun2
1. Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
2. College of Sciences, Guangxi University for Nationalities, Naning 530006, China
 全文: PDF 
摘要： 在初始版本的第一, 二Bianchi恒等式的基础上, 利用二阶或三阶协变导数引申出扩展的二阶协变和三阶协变Bianchi恒等式. 这类二阶协变Bianchi恒等式在黎曼曲率张量沿着两类特殊的几何流-里奇(Ricci)流和双曲几何流的演化方程中有一定的应用. 给出这方面的应用例子并加以阐述.
关键词： 扩展的Bianchi恒等式;  里奇流;  双曲几何流;  黎曼曲率张量演化方程;  共形正规坐标系    
Abstract: Based on the original second Bianchi identity, the authors derive the extended second Bianchi identities via the second or third covariant derivatives. These extended identities have some applications in the evolution equations for the Riemannian or algebraic curvature tensors along two special geometric flows, i.e. the Ricci flow and the hyperbolic geometric flow. Some examples are given to illustrate the related applications.
Key words: extended second Bianchi identity    Ricci flow    hyperbolic geometric flow    evolution equations for the Riemannian curvature tensor    conformal normal coordinates
收稿日期: 2013-07-23 出版日期: 2018-06-10
CLC:  O186.12  
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引用本文:

赵春莉, 卢卫君. 扩展的Bianchi恒等式及其在几何流演化方程中的应用[J]. 高校应用数学学报, 2014, 29(3): 319-332.

ZHAO Chun-li, LU Wei-jun. The extended Bianchi identities and their applications in evolution equations along the geometric flows. Applied Mathematics A Journal of Chinese Universities, 2014, 29(3): 319-332.

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http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2014/V29/I3/319

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