Sharp scalar and Ricci curvature pinching theorems for Lagrangian submanifolds in the homogeneous nearly Kähler Six-sphere

Zejun Hu, Linlin Sun, Jiabin Yin

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…