PreprintCC BY 4.0arXiv
Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere
Abstract
For connected closed Lagrangian submanifolds of the homogeneous nearly Kähler sphere 𝕊6(1), we first establish a new integral inequality. Then, as applications we prove sharp pinching theorems for the scalar curvature τ and Ricci curvature Ric, respectively: τ≥ 23/8 implies either τ=6 with it totally geodesic, or τ=23/8 with it congruent to the embedded Berger sphere of Dillen--Verstraelen--Vrancken; whereas Ric≥1/8 implies that the submanifold is either totally geodesic, or has constant sectional curvature K=1/16, or is congruent to the embedded Berger sphere of Dillen-Verstraelen-Vrancken.
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BibTeX
@misc{hu2026sharp,
title = {{Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere}},
author = {Zejun Hu and Linlin Sun and Jiabin Yin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23470},
eprint = {2609.23470},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23470},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere
AU - Zejun Hu
AU - Linlin Sun
AU - Jiabin Yin
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23470
UR - https://arxiv.org/abs/2609.23470
AB - For connected closed Lagrangian submanifolds of the homogeneous nearly Kähler sphere 𝕊^6(1), we first establish a new integral inequality. Then, as applications we prove sharp pinching theorems for the scalar curvature τ and Ricci curvature Ric, respectively: τ≥ 23/8 implies either τ=6 with it totally geodesic, or τ=23/8 with it congruent to the embedded Berger sphere of Dillen--Verstraelen--Vrancken; whereas Ric≥1/8 implies that the submanifold is either totally geodesic, or has constant sectional curvature K=1/16, or is congruent to the embedded Berger sphere of Dillen-Verstraelen-Vrancken.
ER -