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Эквивалентные подходы к понятию слоения с трансверсальной линейной связностью
Труды Математического центра им. Н.И. Лобачевского. 2013. Т. 47. С. 43-46.
А.Ю. Долгоносова .., Н.И. Жукова
Different equivalent approaches to the notion of a foliation with transverse linear connection are
represented.
Dolgonosova A., Журнал Средневолжского математического общества 2017 Т. 19 № 1 С. 19-29
The subject of this article is a review of the results on foliations with transversal linear connection obtained by the author together with N.I. Zhukova, and their comparison with the results of other authors. The work consists of three parts. The first part focuses on to automorphism groups of foliations with a transversal linear connection ...
Added: June 13, 2017
Zhukova N., Sheina K., Журнал Средневолжского математического общества 2016 Т. 18 № 2 С. 30-40
We find necessary and sufficient conditions for a foliation of codimension $q$ on $n$-dimensional manifold with transverse linear connection to admit a transverse invariant pseudo-Riemannian metric of a given signature which is parallel with the respect to the indicated connection. In particular, we obtain a criterion for a foliation with transverse linear connection to be ...
Added: June 7, 2016
Dolgonosova A., Zhukova N., Журнал Средневолжского математического общества 2015 Т. 17 № 4 С. 14-23
We prove the equivalence of three different approaches to the definition of completeness of a foliation with transverse linear connection. It is shown that for the transverse ane foliations
(M, F) of codimension q, q > 1, each of the mentioned above conditions are equivalent to
fulllment of the following two conditions: 1) there exists an Ehresmann ...
Added: March 12, 2016
Zhukova N., Chebochko N., Известия высших учебных заведений. Математика 2020 № 11 С. 87-92
The aim of this work is to describe the structure of complete Lorentzian foliations $(M, F)$ of codimension two
on $n$-dimensional closed manifolds. It is proved that $(M, F)$ is either Riemannian or has a constant
transversal curvature and its structure is described. For such foliations $(M, F)$, the criterion is obtained,
reducing the chaos problem in $(M, ...
Added: October 6, 2020
Zhukova N., Журнал Средневолжского математического общества 2018 Т. 20 № 4 С. 395-407
It is shown that the structural theory of Molino for Riemannian foliations on compact
manifolds and complete Riemannian manifolds is generalized to Riemannian foliations with
Ehresmann connection. There are no restrictions on the codimension of the foliation
and the dimension of the foliated manifold.
For a Riemannian foliation $(M, F)$ with Ehresmann connection
it is proved that the closure of ...
Added: December 27, 2019
Н.И. Жукова, Шеина К. И., Труды Математического центра им. Н.И. Лобачевского 2014 Т. 50 С. 74-76
We investigate Cartan foliations covered by fibrations. We obtain a sufficient condition for the full
basic automorphism group of a complete Cartan foliation covered by fibration to admit a
unique (finite-dimensional) Lie group structure in the category of
Cartan foliations. The explicit new formula for determining its basic automorphism
Lie group is given. Examples of computing the full basic ...
Added: November 12, 2014
Zhukova N., Труды Московского физико-технического института 2017 Т. 9 № 4 С. 132-141
Complete transversely affine foliations are studied. The strong transversal equivalence of
complete affine foliations is investigated, which is a more refined notion than the transverse
equivalence of foliations in the sense of Molino. A global holonomy group of a complete
affine foliations is determined and it is proved that this group is the complete invariant
of the foliation relatively ...
Added: November 28, 2017
Zhukova N., Математический сборник 2012 Т. 203 № 3 С. 79-106
Доказано, что любое полное конформное слоение (M,F) коразмерности q> 2 является либо римановым, либо (Conf(S^q),S^q)-слоением. Если (M,F) не является римановым слоением, то оно имеет глобальный аттрактор, представляющий собой либо нетривиальное минимальное множество, либо один замкнутый слой или объединение двух замкнутых слоев. При этом компактность многообразия M не предполагается. В частности, каждое собственное полное конформное не риманово ...
Added: September 28, 2014
N. I. Zhukova, Труды Математического института им. В.А. Стеклова РАН 2012 Т. 278 С. 102-113
We prove that any compact manifold whose fundamental group contains an abelian normal subgroup of positive rank can be represented as a leaf of a structurally stable suspended foliation on a compact manifold. In this case, the role of a transversal manifold can be played by an arbitrary manifold. We construct examples of structurally stable ...
Added: September 28, 2014
Н.И. Жукова, Mathematical Notes (Rusian Federation) 2013 Т. 93 № 6 С. 994-996
In this paper a unified method for studying foliations with transversal psrsbolic geometry of rank one is presented.
Ideas of Fraces' paper on parabolic geometry of rank one and of works of the author on conformal foliations
are developed. ...
Added: September 28, 2014
Багаев А. В., Zhukova N., Известия высших учебных заведений. Поволжский регион. Физико-математические науки 2017 № 4 (44) С. 35-47
Actuality and goals. The Lorentzian geometry is radically different from the Riemannian geometry and finds widespread application in various physical theories. The goal of this work is to investigate the structure of transversely analytical Lorentzian foliations (M,F) of codimension two on n-dimensional manifolds.
Methods. The methods of foliated bundles and holonomy pseudogroups are applied.
Results. We prove ...
Added: November 15, 2017
Nina I. Zhukova, Anna Yu. Dolgonosova .., Central European Journal of Mathematics 2013 Vol. 11 No. 12 P. 2076-2088
The category of foliations is considered. In this category
morphisms are differentiable mappings transforming leaves of one
foliation into leaves of the other foliation.
We proved that the automorphism group of the foliations
admitting a transverse linear connection is an infinite-dimensional
Lie group modeled on $LF$-spaces. This result extends the corresponding
result of Macias-Virgos and Sanmartin for Riemannian foliations.
In particular, our ...
Added: September 28, 2014
N. I. Zhukova, Journal of Mathematical Sciences 2016 Vol. 219 No. 1 P. 112-124
We consider a Cartan foliation (M,F) of an arbitrary codimension q admitting an
Ehresmann connection such that all leaves of (M,F) are embedded submanifolds of M.
We prove that for any foliation (M,F) there exists an open, not necessarily connected,
saturated, and everywhere dense subset M0 of M and a manifold L0 such that the induced
foliation (M0, FM0) ...
Added: October 21, 2016
Glutsyuk A., Ergodic Theory and Dynamical Systems 2023
Reflection in a strictly convex bounded planar billiard acts on the space of oriented lines and preserves a standard area form. A caustic is a curve C whose tangent lines are reflected by the billiard to lines tangent to C. The famous Birkhoff conjecture states that the only strictly convex billiards with a foliation by ...
Added: December 29, 2023
Dolgonosova A., Zhukova N., Труды Математического центра им. Н.И. Лобачевского 2015 Т. 52 С. 62-64
Анонсированы следующие результаты о псевдоримановых слоениях:
- новый критерий псевдоримановости слоения произвольной коразмерности на n-мерном псевдоримановом многообразии;
- описание структуры графиков псевдоримановых слоений м мндуцированных на них слоениях. ...
Added: March 12, 2016
N. I. Zhukova, Sbornik Mathematics 2012 Vol. 203 No. 2 P. 380-405
We prove that every complete foliation (M, F) of codimension q > 1 is either Riemannian or a (Conf (S^q), S^q)-foliation. We further prove that if (M, F) is not Riemannian, it has a global attractor which is either a nontrivial minimal set or a closed leaf or a union of two closed leaves. In ...
Added: October 19, 2014
Zhukova N.I., K. I. Sheina, / Cornell University. Series math "arxiv.org". 2015. No. 1410.1144.
We get sufficient conditions for the full basic automorphism group of a complete
Cartan foliation to admit a unique (finite-dimensional) Lie group structure in the category
of Cartan foliations. In particular, we obtain sufficient conditions for this group
to be discrete. Emphasize that the transverse Cartan geometry may be noneffective.
Some estimates of the dimension of this group depending ...
Added: November 10, 2014
Zhukova N., Journal of Physics: Conference Series 2018 Vol. 990 No. 1 P. 1-15
A foliation that admits a Weyl structure arising from a pseudo-Riemannian metric of any signature as its transverse structure is called a pseudo-Riemannian Weyl foliation or (for short) a Weyl foliation. We investigate codimension q ≥ 2 Weyl foliations on (not necessarily compact) manifolds. Different interpretations of their holonomy groups are given. We prove a ...
Added: April 1, 2018
Zhukova N., Journal of Mathematical Sciences 2015 Vol. 208 No. 1 P. 115-130
We study the problem of classification of complete non-Riemannian conformal foliations
of codimension q > 2 with respect to transverse equivalence. It is proved that two
such foliations are transversally equivalent if and only if their global holonomy groups
are conjugate in the group of conformal transformations of the q-dimensional sphere
Conf (Sq). Moreover, any countable essential subgroup of ...
Added: December 11, 2017
Zhukova N., Журнал Средневолжского математического общества 2017 Т. 19 № 4 С. 33-44
For any smooth orbifold $\mathcal N$ is constructed a foliated model, which is a foliation
with an Ehresmann, the leaf space of which is the same as $\mathcal N$. We investigate
the relationship relationship between some properties of orbifold and its foliated model.
The article discusses the application to Cartan orbifolds, that is orbifolds endowed with Cartan geometry. ...
Added: February 20, 2018
Khoroshkin A., Transformation Groups 2015 P. 1-40
We prove the conjecture by Feigin, Fuchs and Gelfand describing the Lie algebra cohomology of formal vector fields on an n-dimensional space with coefficients in symmetric powers of the coadjoint representation. We also compute the cohomology of the Lie algebra of formal vector fields that preserve a given flag at the origin. The latter encodes ...
Added: April 9, 2015
Zhukova N. I., Mathematical notes 2013 Vol. 93 No. 5-6 P. 928-931
In this paper a unified method for studying foliations with transversal parabolic geometry of rank one is presented.
Ideas of Fraces' paper on parabolic geometry of rank one and of works of the author on conformal foliations
are developed. ...
Added: October 19, 2014
Zhukova N. I., Proceedings of the Steklov Institute of Mathematics 2012 Vol. 278 No. 1 P. 94-105
We prove that any compact manifold whose fundamental group contains an abelian normal subgroup of positive rank can be represented as a leaf of a structurally stable suspended foliation on a compact manifold. In this case, the role of a transversal manifold can be played by an arbitrary manifold. We construct examples of structurally stable ...
Added: October 19, 2014