Stability of Complex Foliations Transverse to Fibrations

A Measurable Stability Theorem for Holomorphic Foliations Transverse to Fibrations

Fibrations, Divisors and Transcendental Leaves

We will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of fibrations, the topology of smooth hypersurfaces and the topological closure of transcendental leaves of foliations.

Rigidity of Trivial Actions of Abelian-by-cyclic Groups

The question of existence and stability of global fixed points for group actions has been studied in many different contexts. In the setting of actions of Lie groups it was shown by Lima [8] that n commuting vector fields on a genus g surface, Σg, of non-zero Euler characteristic have a common singularity. This implies that any action of the abelian Lie group R on Σg has a global fixed point. I...

Some Global Results on Holomorphic Lagrangian Fibrations

The globalization of some local structures as the complex Liouville vector field, complex Liouville 1-form, totally singular complex Hamiltonians and complex nonlinear connection on holomorphic Lagrangian fibrations is studied. Also, we give a new characterization of equivalence of two holomorphic Lagrangian foliations. The notions are introduced here by analogy with the real case, see [16, 17,...

The Topology of Foliations Formed by the Generic K-orbits of a Subclass of the Indecomposable Md5-groups

The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to each connected and simply connected MD5-group such that their Lie algebra have 4-dimension commutative derived ideal. In the paper we shall give the topological classification of all considered MD5-foliations. A description of these foliations by fibrations or act...