摘要:
对欧氏空间中的完备自收缩子M,我们证明:如果第二基本形式A满足
![](https://image.hanspub.org/IMAGE/Edit_6d79991e-697d-458f-bec7-fbe737b2ddce.png)
,且平均曲率向量满足
![](https://image.hanspub.org/IMAGE/Edit_5a414f3e-620d-4e58-9f29-e3ec7f1069b7.png)
,那么M等距于下列广义柱面之一
:![](https://image.hanspub.org/IMAGE/Edit_3609a659-56d0-4431-8694-da5df1acecf1.png)
,
![](https://image.hanspub.org/IMAGE/Edit_90cd78a0-17e3-4033-b6c6-9a0fe6cc5521.png)
。
Abstract:
For a complete self-shrinker M in the Eulidean space R
n+p, we prove that if the second fundamental form A satisfies
![](https://image.hanspub.org/IMAGE/Edit_b780f291-b565-4024-86fc-c375a8265441.png)
and the mean curvature H satifies
![](https://image.hanspub.org/IMAGE/Edit_31a33d99-e4a5-4702-8624-5c4e5dc5ef89.png)
, then M is one of the generalized cylinders
![](https://image.hanspub.org/IMAGE/Edit_ad0ab9c7-bcd2-48a9-83ec-b9e41ee41041.png)
,
![](https://image.hanspub.org/IMAGE/Edit_8e84090f-fd1e-48a1-b849-7fd338dad3f7.png)
.