Characterization of Totally Geodesic Totally Real 3-dimensional Submanifolds in the 6-sphere

摘要

In this paper, we study Lagrangian submanifolds of the nearly Kaehler 6-sphere. We derivea pinching result for the Ricci curvature of such submanifolds thus providing a characterisation of thetotally geodesic submanifold. Our pinching result improves a previous result obtained by H. Li.