Vol. 304, No. 2, 2020

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Addendum to the article Contact stationary Legendrian surfaces in $\mathbb{S}^5$

Yong Luo

Vol. 304 (2020), No. 2, 607–611
Abstract

We proved (Pacific J. Math. 293:1 (2018), 101–120) that if L is a contact stationary Legendrian surface in 𝕊5 with the canonical Sasakian structure and the square length of its second fundamental form belongs to [0,2], then 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 𝕊5, then L is totally geodesic.

Keywords
contact stationary surfaces, rigidity
Mathematical Subject Classification 2010
Primary: 53B25
Secondary: 53C42
Milestones
Received: 12 October 2018
Accepted: 4 September 2019
Published: 12 February 2020
Authors
Yong Luo
School of Mathematics and Statistics
Wuhan University
Wuhan
China