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
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.
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.
