Title: A gap theorem for csL surfaces in $S^5$
Speaker: 罗勇 （武汉大学）
Time: 2018年9月14日 上午10:00—11:00
Room: 腾博tengbo988官网研讨室 （信息楼0343）
Abstract: Let $(M^{2n+1},\alpha,g_\alpha,J)$ be a Sasakian Einstein manifold with contact 1-form $\alpha$, associated metric $g_\alpha$ and almost complex structure $J$ and $L$ a Legendrian submanifold in $M^{2n+1}$. $L$ is called a contact stationary Legendrian (csL) submanifold if it is a critical point of the area functional among Legendrian submanifolds. We will prove that csL surfaces in a 5-dimensional Sasakian Einstein manifold satisfies a fourth order quasi-linear elliptic equation and by using this equation and a new Simons' type inequality for Legendrian surfaces in $\mathbb{S}^5$, we get a gap theorem for csL surfaces in $\mathbb{S}^5$, which extends a related gap theorem of minimal Legendrian surfaces in $\mathbb{S}^5$ by Yamaguchi et al..