Minimal Legendrian surfaces in the tangent sphere bundle of 𝕊³

Li, Mingyan; Wang, Yanan

doi:10.1090/proc/16677

Minimal Legendrian surfaces in the tangent sphere bundle of ${\mathbb {S}}^3$
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by Mingyan Li and Yanan Wang;

Proc. Amer. Math. Soc. 152 (2024), 2205-2220

DOI: https://doi.org/10.1090/proc/16677

Published electronically: March 1, 2024

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Abstract:

In this paper we study minimal Legendrian surfaces $\Sigma$ immersed in tangent sphere bundle $T_1{\mathbb {S}}^3$. We classify (1) totally geodesic Legendrian surfaces, (2) closed minimal Legendrian surfaces of genus smaller than or equal to one and complete minimal Legendrian surfaces with non-negative Gauss curvature.

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