Toshikazu Ito

A NON-EXISTENCE THEOREM FOR MORSE TYPE HOLOMORPHIC FOLIATIONS OF CODIMENSION ONE TRANSVERSE TO SPHERES

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.

On the classification of non-integrable complex distributions

We study the classification of singularities of holomorphic foliations and non-integrable one-forms under the hypothesis of transversality with real hypersurfaces.We study the classification of singularities of holomorphic foliations and non-integrable one-forms under the hypothesis of transversality with real hypersurfaces.

On holomorphic one-forms transverse to closed hypersurfaces

In this note we announce some achievements in the study of holomorphic distributions admitting transverse closed real hypersurfaces. We consider a domain with smooth boundary in the complex affine space of dimension two or greater. Assume that the domain satisfies some cohomology triviality hypothesis (for instance, if the domain is a ball). We prove that if a holomorphic one form in a neighborhood of the domain is such that the corresponding holomorphic distribution is transverse to the boundary of the domain then the Euler-Poincare-Hopf characteristic of the domain is equal to the sum of indexes of the one-form at its singular points inside the domain. This result has several consequences and applies, for instance, to the study of codimension one holomorphic foliations transverse to spheres.

On holomorphic flows on Stein surfaces: Transversality, dicriticalness and stability

We study the classification of the pairs

A Poincaré–Hopf-type theorem for holomorphic one-forms

(N, \,X)

Transversality of complex linear distributions with spheres, contact forms and Morse type foliations

where

Holomorphic foliations transverse to manifolds with corners

N

On the Geometry of Holomorphic Flows and Foliations Having Transverse Sections

is a Stein surface and

Holomorphic foliations of codimension one transverse to polydiscs

X

Transversality of complex linear distributions with spheres, contact forms and Morse type foliations, II

is a complete holomorphic vector field with isolated singularities on