Addendum to "Contact stationary Legendrian surfaces in $\mathbb{S}^5$"[Pacific Math. J. 293(2018), no.1, 101-120]

Yong Luo

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arXiv · 1712.05100

Addendum to "Contact stationary Legendrian surfaces in $\mathbb{S}^5$"[Pacific Math. J. 293(2018), no.1, 101-120]

Yong Luo

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Abstract

In \cite{Luo}, the present author proved that if $L$ is a contact stationary Legendrian surface in $\mathbb{S}^5$ with the canonical Sasakian structure and the square length of its second fundamental form belongs to $[0,2]$. Then we have that $L$ is either totally umbilical or is a flat minimal Legendrian torus. In this addendum we further prove that if $L$ is a totally umbilical contact stationary Legendrian surface in $\mathbb{S}^5$ , then $L$ is totally geodesic.

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BibTeX RIS

Yong Luo. 2017-12-14. Addendum to "Contact stationary Legendrian surfaces in $\mathbb{S}^5$"[Pacific Math. J. 293(2018), no.1, 101-120]. https://arxiv.org/abs/1712.05100

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