在三維閉CR流型上CR Yamabe流的長時間存在性

The Long Time Existence for the CR Yamabe Flow on Closed CR Manifolds of Dimension Three

呂心宇(Hsin-Yu Lu)

指導教授 ： 張樹城

國立清華大學/理學院/數學系/碩士(2007年)

https://doi.org/10.6843/NTHU.2007.00173

摘要

我們考慮正規化的 CR Yamabe 流 $frac{partial heta
(t)}{partial t} = 2(r(t) -
ho (t)) heta(t)$, 而 $ heta (t)$
是在一閉 CR 流型 $M$ 上的一族 contact forms, $
ho (t)$ 記為它之
Tanaka-Webster 曲率, 以及 $r(t) = frac{int_M
ho(t) heta(t)
wedge d heta(t)}{int_M 1 heta(t) wedge d heta(t)}$.
我們將證明當$M$的維數是三時, 這個流有長時間存在性. 特別對於
常曲率不為正的情形下, 我們能說明這個流會收斂.

關鍵字

CR ； Yamabe Flow ； 長時間

並列摘要

We consider the normalized CR Yamabe flow
$frac{partial heta (t)}{partial t} = 2(r(t) -
ho (t)) heta
(t)$, where $ heta (t)$ is a family of contact forms on a closed CR
manifold $M$, $
ho (t)$ denotes its Tanaka-Webster curvatures, and
$r(t) = frac{int_M
ho(t) heta(t) wedge d heta(t)}{int_M 1
heta(t) wedge d heta(t)}$. We will show this flow has the long
time existence when $M$ is of dimension three. In particular for the
scalar negative case and the scalar flat case, we can show the
asymptotic convergence for our flow.

並列關鍵字

CR ； Yamabe Flow ； Long Time

參考文獻

[6] Shu-Cheng Chang, Hung-Lin Chiu, and Chin-Tung Wu, The Li-

[1] Simon Brendle, Convergence of the Yamabe Flow for Arbitrary

the Yamabe Flow on CR Manifolds of Dimension 3, Annals of

[3] Sorin Dragomir and Giuseppe Tomassini, Differential Geometry

and Analysis on CR Manifolds, Birkhaeuser