Quasi-Einstein totally real submanifolds of the nearly Kähler 6-sphere
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 \textit{F. Dillen} and \textit{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 \(S^6\).
scientific article; zbMATH DE number 1445638
scientific article