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| Evolution Equations of Curvature Tensors Along theHyperbolic Geometric Flow |
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Citation： |
Weijun LU.Evolution Equations of Curvature Tensors Along theHyperbolic Geometric Flow[J].Chinese Annals of Mathematics B,2014,35(6):955~968 |
| Page view： 1354
Net amount： 1020 |
Authors： |
Weijun LU; |
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| Abstract： |
The author considers the hyperbolic geometric flow
$\frac{\partial^2}{\partial t^2}g(t)=-2{\rm Ric}_{g(t)}$ 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. |
Keywords： |
Hyperbolic geometric flow, Evolution equations, Singularity |
Classification： |
53C21, 53C44, 58J45 |
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