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This article is available for purchase or by subscription. See below.
Abstract
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We proved (Pacific J. Math. 293:1 (2018), 101–120) that if
is a contact stationary
Legendrian surface in
with the canonical Sasakian structure and the square length of its second fundamental form
belongs to
,
then
is
either totally umbilical or is a flat minimal Legendrian torus. In this addendum we further
prove that if
is a totally umbilical contact stationary Legendrian surface in
, then
is
totally geodesic.
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Keywords
contact stationary surfaces, rigidity
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Mathematical Subject Classification 2010
Primary: 53B25
Secondary: 53C42
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Milestones
Received: 12 October 2018
Accepted: 4 September 2019
Published: 12 February 2020
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