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

Author:

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

Abstract

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

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. Totally real submanifolds in a 6-sphere;Ejiri, Norio;Proc. Amer. Math. Soc.,1981

2. Zur Differentialgeometrie der komplexen Strukturen;Frölicher, Alfred;Math. Ann.,1955

3. Almost Hermitian structure on 𝑆⁶;Fukami, Tetsuzo;Tohoku Math. J. (2),1955

4. Minimal varieties and almost Hermitian submanifolds;Gray, Alfred;Michigan Math. J.,1965

5. A characterization of seven compact Kaehler submanifolds by holomorphic pinching;Ros, Antonio;Ann. of Math. (2),1985

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