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Группы базовых автоморфизмов картановых слоений, накрытых расслоениями
Труды Математического центра им. Н.И. Лобачевского. 2014. Т. 50. С. 74-76.
Н.И. Жукова, Шеина К. И.
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 automor\phism group of complete Cartan foliations are constructed.
Sheina K., Известия высших учебных заведений. Поволжский регион. Физико-математические науки 2021 Т. 1 № 1 С. 49-65
The basic automorphism group of a Cartan foliation (M,F) is the quotient group of the automorphism group of (M, F ) by the normal subgroup, which preserves every leaf invariant. For Cartan foliations covered by fibrations, we find sufficient conditions for the existence of a structure of a finite-dimensional Lie group in their basic automorphism ...
Added: December 16, 2020
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
Группы базовых автоморфизмов картановых слоений моделируемых на неэффективных картановых геометриях.
Zhukova N., Sheina K., Труды Математического центра им. Н.И. Лобачевского 2015 Т. 52 С. 73-74
Исследуются картановы слоения, то есть слоения допускающие трансверсальную картанову геометрию. Рассматривается общая ситуация, когда картанова геометрия может быть неэффективной. Найдено достаточное условие для того, чтобы полная группа базовых автоморфизмов картанова слоения со связностью Эресмана допускала единственную структуру конечномерной группы Ли в категории картановых слоений, где изоморфизмы сохраняют как слоение, так и трансверсальную геометрию. Получены некоторые ...
Added: October 14, 2015
Sheina K., Zhukova N., Lobachevskii Journal of Mathematics 2016
For a complete Cartan foliation $(M,F)$ we introduce two algebraic invariants $\frak{g}_{0}(M,F)$ and
${\frak g}_{1}(M,F)$ which we
call structure Lie
algebras. If the transverse Cartan geometry of $(M,F)$ is effective then
$\frak{g}_{0}(M,F)={\frak g}_{1}(M,F)$. We prove that if $\frak{g}_{0}(M,F)$
is zero then in the category of Cartan foliations the group of all basic automorphisms of the ...
Added: October 12, 2016
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., 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
/ Cornell University. Series arXiv "math". 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 ...
Added: September 28, 2015
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
Bazaikin Y., Galaev A., Zhukova N., Chaos 2020 Vol. 30 P. 1-9
Chaotic foliations generalize Devaney's concept of chaos for
dynamical systems. The property of a foliation to
be chaotic is transversal. The existence problem of chaos for a Cartan foliation
is reduced to the corresponding problem for its holonomy pseudogroup of
local automorphisms of a transversal manifold. Chaotic foliations with transversal Cartan ...
Added: October 6, 2020
K. I. Sheina, N. I. Zhukova, Lobachevskii Journal of Mathematics 2018 Vol. 39 No. 2 P. 271-280
For a complete Cartan foliation (M; F) we introduce
two algebraic invariants g0(M; F) and g1(M; F) which we call structure
Lie algebras. If the transverse Cartan geometry of (M; F) is eective
then g0(M; F) = g1(M; F). We prove that if g0(M; F) is zero then in
the category of Cartan foliations the group of all basic ...
Added: March 23, 2017
Nina. I. Zhukova, Galaev A., / Cornell University. Series math "arxiv.org". 2017.
The paper is focused on the existence problem of attractors for foliations. Since the existence of an attractor is a transversal property of the foliation, it is natural to consider foliations admitting transversal geometric structures. As transversal structures are chosen Cartan geometries due to their universality. The existence problem of an attractor on a complete ...
Added: March 23, 2017
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
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
Sheina K., / Cornell University. Series arXiv "math". 2020. No. 04348v1.
The basic automorphism group of a Cartan foliation (M, F) is the quotient group of the automorphism group of (M, F) by the normal subgroup, which preserves every leaf invariant. For Cartan foliations covered by fibrations, we find sufficient conditions for the existence of a structure of a finite-dimensional Lie group in their basic automorphism groups. Estimates ...
Added: December 9, 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
А.Ю. Долгоносова .., Н.И. Жукова, Труды Математического центра им. Н.И. Лобачевского 2013 Т. 47 С. 43-46
Different equivalent approaches to the notion of a foliation with transverse linear connection are
represented. ...
Added: October 18, 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
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
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
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
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., 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
Przyjalkowski V., Shramov K., Математический сборник 2021 Т. 212 № 3 С. 112-127
Показано, что действие любой редуктивной подгруппы в группе автоморфизмов квазигладкого хорошо сформированного взвешенного полного пересечения размерности не меньше 3 индуцировано действием подгруппы в группе автоморфизмов объемлющего взвешенного проективного пространства. Приведены примеры, показывающие, что группа автоморфизмов квазигладкого хорошо сформированного взвешенного полного пересечения Фано может быть бесконечной и даже нередуктивной. ...
Added: March 5, 2021
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