Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere
Year: 2026
Type: preprint
Abstract: For connected closed Lagrangian submanifolds of the homogeneous nearly Kähler sphere $\mathbb S^6(1)$, 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: $τ\ge \tfrac{23}{8}$ implies either $τ=6$ with it totally geodesic, or $τ=\tfrac{23}{8}$ with it congruent to the embedded Berger sphere of Dillen--Verstraelen--Vrancken; whereas ${\rm Ric}\geq\frac18$ implies that the submanifold is either totally geodesic, or has constant sectional curvature $K=\tfrac{1}{16}$, or is congruent to the embedded Berger sphere of Dillen-Verstraelen-Vrancken.
Source: arXiv (Cornell University)
Authors: Hu, Zejun, Sun, Linlin, Yin, Jiabin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214029569