The Legendrian Self-Expander in the Standard Contact Euclidean Five-space
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Abstract
Based on the geometric correspondence between Lagrangian and Legendrian submanifolds, we construct Legendrian 2-submanifolds in the standard contact Euclidean Five-space $\mathbb{R}^{5} $ satisfying the self-similarity equation $H+\theta\xi=\alpha{F}^{\perp}(\alpha>0) $, with particular focus on their self-expander solutions under Legendrian mean curvature flow. This paper mainly generalizes Theorem C of the work by Joyce-Lee-Tsui.
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