扩展的Bianchi恒等式及其在几何流演化方程中的应用  

The extended Bianchi identities and their applications in evolution equations along the geometric flows

作　　者：赵春莉[1] 卢卫君[2] 

机构地区：[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

出　　处：《高校应用数学学报（A辑）》2014年第3期319-332,共14页Applied Mathematics A Journal of Chinese Universities(Ser.A)

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.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.

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 

分 类 号：O186.12[理学—数学] O189.3[理学—基础数学]