Convergence of Finslerian metrics under Ricci flow
Convergence of Finslerian metrics under Ricci flow
摘要
In this work,we study the convergence of evolving Finslerian metrics first in a general flow and next under Finslerian Ricci flow.More intuitively it is proved that a family of Finslerian metrics g（t）which are solutions to the Finslerian Ricci flow converges in C~∞ to a smooth limit Finslerian metric as t approaches the finite time T.As a consequence of this result one can show that in a compact Finsler manifold the curvature tensor along the Ricci flow blows up in a short time.
在这个工作，我们学习在 Finslerian Ricci 流动下面在一般流动并且下次首先发展 Finslerian 度量标准的集中。更直觉地，是 Finslerian Ricci 的答案的 Finslerian 度量标准 g (t) 的一个家庭流动，这被证明当 t 接近有限时间 T，在 C <sup></sup> 收敛到一个光滑的限制 Finslerian 度量标准。作为这结果的后果，一个人能在紧缩的 Finsler 显示出那歧管沿着 Ricci 流动的弯曲张肌在一短时间骤起。
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