In this article, we first describe codimension two regular foliations with
numerically trivial canonical class on complex projective manifolds whose
canonical class is not numerically effective. Building on a recent algebraicity
criterion for leaves of algebraic foliations, we then address regular
foliations of small rank with numerically trivial canonical class on complex
projective manifolds whose canonical class is pseudo-effective. Finally, we
confirm the generalized Bondal conjecture formulated by Beauville in some
special cases.
Comment: 20 pages