On totally real 3-dimensional submanifolds of the nearly Kaehler 6-sphere

Dillen, F.; Opozda, B.; Verstraelen, L.; Vrancken, L.

doi:10.1090/S0002-9939-1987-0877050-8

On totally real $3$-dimensional submanifolds of the nearly Kaehler $6$-sphere
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by F. Dillen, B. Opozda, L. Verstraelen and L. Vrancken PDF

Proc. Amer. Math. Soc. 99 (1987), 741-749 Request permission

Abstract:

Let $M$ be a compact $3$-dimensional totally real submanifold of the nearly Kaehler $6$-dimensional unit sphere. Let $K$ be the sectional curvature function of $M$. Then, if $K > 1/16$, $M$ is a totally geodesic submanifold (and $K \equiv 1$).

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