A remark on foliations on a complex projective space with complex leaves (Q1202797)

Let \(P_{n+p}(\mathbb{C})\) be an \((n+p)\)-dimensional complex projective space with Fubini-Study metric of constant holomorphic sectional curvature \(c\). Let \(F\) be a complex foliation on \(P_{n+p}(\mathbb{C})\) with codimension \(p\) and let \(S\) be the length of the second fundamental form of \(F\). Then the author proves that if the normal distribution of \(F\) is minimal and \(S<(n+2)/(4-1/p)\), then \(F\) is totally geodesic.