Evolution Equations of Curvature Tensors Along the Hyperbolic Geometric Flow

The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms of evolution equations for Levi-Civita connection and curvature tensors under the hy...

Full description

Saved in:
Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 35; no. 6; pp. 955 - 968
Main Author Lu, Weijun
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014
Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
School of Science, Guangxi University for Nationalities, Naning 530006, China
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
Ricci曲率
双曲几何
双曲线
曲率张量
有限时间
演化方程
类似
联络
Singularity
Evolution equations
58J45
53C44
Hyperbolic geometric flow
53C21
Online AccessGet full text

Cover

More Information
Summary:The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms of evolution equations for Levi-Civita connection and curvature tensors under the hyperbolic geometric flow. In addition, similarly to the Ricci flow case, it is shown that any solution to tile hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.
Bibliography:Hyperbolic geometric flow, Evolution equations, Singularity
The author considers the hyperbolic geometric flow introduced by Kong and Liu. Using the techniques and ideas to deal with the evolution equations along the Ricci flow by Brendle, the author derives the global forms of evolution equations for Levi-Civita connection and curvature tensors under the hyperbolic geometric flow. In addition, similarly to the Ricci flow case, it is shown that any solution to tile hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.
31-1329/O1
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-014-0861-9