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A smooth foliation of the 5-sphere by complex surfaces. (English) Zbl 1029.32019

Ann. Math. (2) 156, No. 3, 915-930 (2002); corrigendum ibid. 174, No. 3, 1951-1952 (2011).
The authors construct an example of a smooth codimension one foliation \(\mathcal F\) on the sphere \({\mathbf S}^5\) whose tangent \(T{\mathcal F}\) has an integrable almost complex structure; that is, they construct a smooth, codimension one, integrable and Levi flat CR-structure on \({\mathbf S}^5\). This CR-structure is not embeddable in any Stein space nor Kähler manifold.
The construction is a smart modification of the first example of a smooth codimension one foliation of \({\mathbf S}^5\), discovered by H. B. Lawson [Ann. Math. (2) 94, 494-503 (1971; Zbl 0236.57014)].

MSC:

32V30 Embeddings of CR manifolds
57R30 Foliations in differential topology; geometric theory

Citations:

Zbl 0236.57014
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