On real submanifolds of Kähler manifolds foliated by complex submanifolds
Let \(X\) be a Kähler manifold, \(M\) a compact orientable real submanifold of \(X\), and suppose that \(M\) admits a foliation \(\mathfrak F\) whose leaves are complex submanifolds of \(X\) with complex dimension \(p\). The authors prove that if the \(p\)-th power of the Kähler form of \(X\) is exact when restricted to \(M\), then \(\mathfrak F\) has no nontrivial foliation cycles. Some applications are given and it is stated that analogous results hold in symplectic and contact geometry.
scientific article; zbMATH DE number 597317