A sharp pinching theorem for closed minimal Legendrian submanifolds

Yong Luo; Linlin Sun; Jiabin Yin

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arXiv · 2610.18536

A sharp pinching theorem for closed minimal Legendrian submanifolds

Yong Luo·Linlin Sun·Jiabin Yin

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Abstract

Let $F:M^n\to\mathbb{S}^{2n+1}$ be a minimal Legendrian immersion of a connected closed manifold, where $n\ge3$, and let $B$ be its second fundamental form. We prove that if $|B|^2\le(n-1)(n+2)/n$, then, up to a unitary transformation, $F$ parametrizes a totally geodesic sphere or is a finite covering of the image of the minimal Calabi product of a point and a totally geodesic Legendrian sphere. This proves Conjecture 1 of Luo and Sun [Ann. Inst. H. Poincaré C Anal. Non Linéaire 40 (2023), p. 548].

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BibTeX RIS

Yong Luo, Linlin Sun, Jiabin Yin. 2026-10-13. A sharp pinching theorem for closed minimal Legendrian submanifolds. https://arxiv.org/abs/2610.18536

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