Marek Grochowski
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View article: On the existence and prolongation of infinitesimal isometries on special sub-Riemannian manifolds
On the existence and prolongation of infinitesimal isometries on special sub-Riemannian manifolds Open
In the present paper we deal with (local) infinitesimal isometries of special sub-Riemannian manifolds (a contact and oriented sub-Riemannian manifold is called special if the Reeb vector field is an isometry). The objective of the paper i…
View article: On the dimension of the algebras of local infinitesimal isometries of 3-dimensional special sub-Riemannian manifolds
On the dimension of the algebras of local infinitesimal isometries of 3-dimensional special sub-Riemannian manifolds Open
Suppose that we are given a contact sub-Riemannian manifold ( M , H , g ) of dimension 3 such that the Reeb vector field is an infinitesimal isometry (such manifolds will be referred to as special). For a point $$q\in M$$ denote by $$…
View article: A de Rham decomposition type theorem for contact sub-Riemannian manifolds
A de Rham decomposition type theorem for contact sub-Riemannian manifolds Open
In this paper we prove a result which can be regarded as a sub-Riemannian version of de Rham decomposition theorem. More precisely, suppose that ( M , H , g ) is a contact and oriented sub-Riemannian manifold such that the Reeb vector fiel…
View article: System and Human Safety: Critical Infrastructure and Anti-Terrorist Attachment
System and Human Safety: Critical Infrastructure and Anti-Terrorist Attachment Open
The critical infrastructure (CI) has an important place in Polish security system. The article discusses legal acts and characterises the notion of critical infrastructure as an element essential for the functioning of the society. As a re…
View article: System and Human Safety: Critical Infrastructure and Anti-Terrorist Attachment
System and Human Safety: Critical Infrastructure and Anti-Terrorist Attachment Open
The magazine's publications deal with issues related to work safety. Both in the area of occupational health and safety, organization of the workplace (technical aspects) and the environment (environmental factors in working conditions). T…
View article: On contact sub-pseudo-Riemannian isometries
On contact sub-pseudo-Riemannian isometries Open
We study isometries in the contact sub-pseudo-Riemannian geometry. In particular we give an upper bound on the dimension of the isometry group of a general sub-pseudo-Riemannian manifold and prove that the maximal dimension is attained for…
View article: 3-dimensional left-invariant sub-Lorentzian contact structures
3-dimensional left-invariant sub-Lorentzian contact structures Open
We provide a classification of $ts$-invariant sub-Lorentzian structures on $3$ dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection.
View article: Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds
Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds Open
In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector…
View article: Invariants of contact sub-pseudo-Riemannian structures and Einstein-Weyl geometry
Invariants of contact sub-pseudo-Riemannian structures and Einstein-Weyl geometry Open
We consider local geometry of sub-pseudo-Riemannian structures on contact manifolds. We construct fundamental invariants of the structures and show that the structures give rise to Einstein-Weyl geometries in dimension 3, provided that cer…