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pro vyhledávání: '"Galaev, Anton S."'
We prove that if a simply connected non-conformally flat conformal Lorentzian manifold $(M,c)$ admits an essential transitive group of conformal transformations, then there exists a metric $g\in c$ such that $(M,g)$ is a complete homogeneous plane wa
Externí odkaz:
http://arxiv.org/abs/2407.03095
Autor:
Ernst, Igor, Galaev, Anton S.
Publikováno v:
Collectanea Mathematica 2024
We describe Lorentzian manifolds that admit metric connections with parallel torsion having zero twistorial component and non-zero vectorial component. We also describe Lorentzian manifolds admitting metric connections with closed parallel skew-symme
Externí odkaz:
http://arxiv.org/abs/2303.13288
Publikováno v:
The Journal of Geometric Analysis 34, 282 (2024)
We find the local form of all non-closed Lorentzian Weyl manifolds $(M,c,\nabla)$ with recurrent curvature tensor.If the dimension of the manifold is greater than 3, then the conformal structure is flat, and the recurrent Weyl structure is locally de
Externí odkaz:
http://arxiv.org/abs/2204.10163
Autor:
Ernst, Igor, Galaev, Anton S.
Publikováno v:
Documenta Mathematica 27 (2022), 2333-2383
The paper is devoted to metric connections with parallel skew-symmetric torsion in Lorentzian signature. This is motivated by recent progress in the Riemannian signature and by possible applications to supergravity theories. We provide a complete inf
Externí odkaz:
http://arxiv.org/abs/2202.05616
Autor:
Dikarev, Andrei, Galaev, Anton S.
Publikováno v:
Monatshefte f\"ur Mathematik 196 (2021), 39--58
Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel spinors are found. For Lorentzian Weyl manifolds admitting recurrent null vector fields are introduced special local coordinates similar to Kundt and Walker ones. Using that,
Externí odkaz:
http://arxiv.org/abs/2007.07615
Publikováno v:
Mathematische Zeitschrift 300 (2022), 1335--1349
The paper deals with a modified Godbillon-Vey class defined by Losik for codimension-one foliations. This characteristic class takes values in the cohomology of the second order frame bundle over the leaf space of the foliation. The definition of the
Externí odkaz:
http://arxiv.org/abs/1912.01267
Akademický článek
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Publikováno v:
Journal of the Institute of Mathematics of Jussieu 21 (2022), 1391--1419
Following Losik's approach to Gelfand's formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions for non-triviality in terms of dynamical properties
Externí odkaz:
http://arxiv.org/abs/1810.01143
Autor:
Galaev, Anton S.
It is shown that the characteristic classes of foliations that were defined by Losik and that take values in the de~Rham cohomology of the space of infinite order frames over the leaf space may be mapped to the characteristic classes with values in t
Externí odkaz:
http://arxiv.org/abs/1709.05888
Autor:
Galaev, Anton S., Zhukova, Nina I.
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 transversa
Externí odkaz:
http://arxiv.org/abs/1703.07597