Totally real submanifolds in a 6-sphere
Consider the 6-dimensional Riemannian sphere \(S^ 6\) with constant curvature 1 endowed with the nearly Kähler structure induced from the Cayley divison algebra. Suppose that \(M\) is a 3-dimensional compact totally real submanifold of \(S^ 6\) and let \(k_ 0\) be the infimum of the sectional curvature of \(M\). The author proves that either \(4k_ 0\leq 1\) or \(M\) is totally geodesic.
scientific article; zbMATH DE number 59879