On Ricci Curvature Pinching of Lagrangian Submanifolds in the Homogeneous Nearly Kähler $$\pmb {\mathbb {S}}^6(1)$$

Abstract

In this short paper, we study compact Lagrangian submanifolds of the homogeneous nearly Kahler 6-dimensional unit sphere $${\mathbb {S}}^6(1)$$. Following a strategy in Hu et al. (J Geom Phys 144:199–208, 2019), we shall establish an optimal pinching theorem in terms of the Ricci curvature so that a new characterization of the totally geodesic $${\mathbb {S}}^3(1)$$ and the Dillen–Verstraelen–Vrancken’s Berger sphere $$S^3$$ (described in J Math Soc Jpn 42:565–584, 1990) in $${\mathbb {S}}^6(1)$$ can be given.