Evolution Equations of Curvature Tensors Along theHyperbolic Geometric Flow |
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Authors: | Weijun LU |
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Affiliation: | School of Science, Guangxi University for Nationalities, Naning 530006, China;Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China |
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Abstract: | The author considers the hyperbolic geometric flow (tfrac{{partial ^2 }} {{partial t^2 }}g(t) = - 2Ric_{g(t)}) 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 the hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature. |
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Keywords: | Hyperbolic geometric flow Evolution equations Singularity |
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