PreprintCC BY 4.0arXiv
A sharp pinching theorem for closed minimal Legendrian submanifolds
Abstract
Let F:Mn→𝕊2n+1 be a minimal Legendrian immersion of a connected closed manifold, where n≥3, and let B be its second fundamental form. We prove that if |B|2≤(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
@misc{luo2026sharp,
title = {{A sharp pinching theorem for closed minimal Legendrian submanifolds}},
author = {Yong Luo and Linlin Sun and Jiabin Yin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18536},
eprint = {2610.18536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18536},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A sharp pinching theorem for closed minimal Legendrian submanifolds
AU - Yong Luo
AU - Linlin Sun
AU - Jiabin Yin
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18536
UR - https://arxiv.org/abs/2610.18536
AB - Let F:M^n→𝕊^2n+1 be a minimal Legendrian immersion of a connected closed manifold, where n≥3, and let B be its second fundamental form. We prove that if |B|^2≤(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].
ER -