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Quasi-Einstein totally real submanifolds of the nearly Kähler 6-sphere. (English) Zbl 0990.53014

The authors investigate 3-dimensional totally real quasi-Einstein submanifolds of the nearly Kähler 6-sphere \(S^6\). (A submanifold in \(S^6\) is said to be totally real if the almost complex structure \(J\) on \(S^6\) interchanges the tangent and the normal space. An \(n\)-dimensional manifold whose Ricci tensor has an eigenvalue of multiplicity at least \(n-1\) is said to be quasi-Einstein.) Necessary and sufficient conditions for a totally real \(M_3 \subset S^6\) to be quasi-Einstein are derived, examples of these submanifolds are constructed by considering tubes with different radii. The results of this paper together with the classification theorems in F. Dillen and L. Vrancken [Trans. Am. Math. Soc. 348, 1633-1646 (1996; Zbl 0882.53017)] provide a complete classification of the totally real quasi-Einstein submanifolds of \(S^6\).

MSC:

53B25 Local submanifolds

Citations:

Zbl 0882.53017
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References:

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