6,675 research outputs found
Vector field construction of Segre sets
A CR generic real analytic CR manifold M carries two families of Segre
varieties and conjugate Segre varieties. We observe in this article that their
complexifications give rise to two families of foliations of the
complexification of M which coincide with the flow foliations induced by the
complexified CR (1,0) and (0,1) vector fields tangent to M. As an application,
we derive a new proof of the characterization of finite type in terms of Segre
sets.Comment: Completely rewritten version, 42 pages Sujclass: Complex Variable
Commuting foliations
The aim of this paper is to extend the notion of commutativity of vector
fields to the category of singular foliations, using Nambu structures, i.e.
integrable multi-vector fields. We will classify the relationship between
singular foliations and Nambu structures, and show some basic results about
commuting Nambu structures.Comment: New version, with a completely new section which clarifies the
relationship between singular foliations and Nambu structures. The size of
the paper has doubled from 10 to 20 page
On the connectedness of the space of codimension one foliations on a closed 3-manifold
We study the topology of the space of smooth codimension one foliations on a
closed 3-manifold. We regard this space as the space of integrable plane fields
included in the space of all smooth plane fields. It has been known since the
late 60's that every plane field can be deformed continuously to an integrable
one, so the above inclusion induces a surjective map between connected
components. We prove that this map is actually a bijection.Comment: 47 pages, 22 figure
Foliations of Tangent Bundle in a Finsler Manifold
In this paper, a frame is introduced on tangent bundle of a Finsler manifold
in a manner that it makes some simplicity to study the properties of the
natural foliations in tangent bundle. Moreover, we show that the indicatrix
bundle of a Finsler manifold with lifted sasaki metric and natural almost
complex structure on tangent bundle cannot be a sasakian manifold.Comment: 11 pages. arXiv admin note: substantial text overlap with
arXiv:1106.482
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