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The Ricci curvature of totally real 3-dimensional submanifolds of the nearly Kaehler 6-sphere. (English) Zbl 0853.53037

Let \(M\) be a compact 3-dimensional totally real submanifold of the nearly Kaehler 6-sphere. The author proves that if the Ricci curvature Ric of \(M\), defined by \(\text{Ric} (v)= \sum \langle R(e_i, v)v, e_i \rangle\) satisfies \(\text{Ric} \geq 53/64\), then \(M\) is totally geodesic and \(\text{Ric}=2\).
Reviewer: F.Dillen (Leuven)

MSC:

53C40 Global submanifolds
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