Second variation and Legendrian stabilities of minimal Legendrian submanifolds in Sasakian manifolds
Second variation and Legendrian stabilities of minimal Legendrian submanifolds in Sasakian manifolds
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DOI：
10.1016/j.difgeo.2005.01.007
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发表时间：
2005-05
影响因子：
0.5
通讯作者：
Hajime Ono
中科院分区：
文献类型：
--
作者：
Hajime Ono
首先，我们得到一个新的第二变分公式，它适用于Sasakian流形中的极小Legendrian子流形。利用这一点，我们证明了具有“非正”η-Ricci常数的η-Einstein Sasakian流形中的任何极小Legendrian子流形都是稳定的.接下来我们引入Sasakian流形中极小Legendrian子流形的Legendrian稳定性的概念。利用我们的第二变分公式，得到了具有“正”η-Ricci常数的η-Einstein Sasakian流形中极小Legendrian子流形的Legendrian稳定性的一般判据.
First, we derive a new second variation formula which holds for minimal Legendrian submanifolds in Sasakian manifolds. Using this, we prove that any minimal Legendrian submanifold in an η-Einstein Sasakian manifold with “nonpositive”η-Ricci constant is stable. Next we introduce the notion of the Legendrian stability of minimal Legendrian submanifolds in Sasakian manifolds. Using our second variation formula, we find a general criterion for the Legendrian stability of minimal Legendrian submanifolds in η-Einstein Sasakian manifolds with “positive”η-Ricci constant.