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

Authors: F. Dillen, B. Opozda, L. Verstraelen and L. Vrancken
Journal: Proc. Amer. Math. Soc. 99 (1987), 741-749
MSC: Primary 53C40
MathSciNet review: 877050
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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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