A non-existence theorem for Morse type holomorphic foliations of codimension one transverse to spheres
نویسندگان
چکیده
We prove that a Morse type codimension one holomorphic foliation is not transverse to a sphere in the complex affine space. Also we characterize the variety of contacts of a linear foliation with concentric spheres.
منابع مشابه
On Holomorphic Foliations Transverse to Spheres
We study the problem of existence and classification of holomorphic foliations transverse to a real submanifold in the complex affine space. In particular we investigate the existence of a codimension one holomorphic foliation transverse to a sphere in C for n ≥ 3. 2000 Math. Subj. Class. Primary 32S65; Secondary 57R30.
متن کاملOn holomorphic foliations with projective transverse structure
We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic motivation is the characterization of pull-backs of Riccati foliations on projective spaces. Our techniques apply to give a description of th...
متن کاملStability of Holomorphic Foliations with Split Tangent Sheaf
We show that the set of singular holomorphic foliations on projective spaces with split tangent sheaf and good singular set is open in the space of holomorphic foliations. We also give a cohomological criterion for the rigidity of holomorphic foliations induced by group actions and prove the existence of rigid codimension one foliations of degree n − 1 on P for every n ≥ 3.
متن کاملOn smooth foliations with Morse singularities
Let M be a smooth manifold and let F be a codimension one, C foliation on M , with isolated singularities of Morse type. The study and classification of pairs (M,F) is a challenging (and difficult) problem. In this setting, a classical result due to Reeb [Reeb] states that a manifold admitting a foliation with exactly two centertype singularities is a sphere. In particular this is true if the f...
متن کاملThéorème de Bochner et feuilletage minimal
The starting point of this work is the Bochner theorem on harmonics 1-forms stated at 1946. We show that many results on minimal foliations of codimension one and two on compact pseudo-Riemannian manifolds are at the origin of this theorem. We also prove the non existence of minimal Riemannian foliations of codimension one defined by a 1-form with finite global norm on complete non compact Riem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008