|
This article is cited in 3 scientific papers (total in 3 papers)
Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds
Marek Grochowskiab, Ben Warhurstc a Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszyński University, ul. Dewajtis 5, 01-815 Waszawa, Poland
b Institute of Mathematics, Polish Academy of Sciences,
ul. Śniadeckich 8, 00-950 Warszawa, Poland
c Institute of Mathematics, The Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Abstract:
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 fields which generate isometric and conformal symmetries in general sub-Lorentzian manifolds. We then focus attention back to the case where the underlying manifold is a contact $3$ manifold and more specifically when the manifold is also a Lie group and the structure is left-invariant.
Keywords:
sub-Lorentzian; contact distribution; left-invariant; symmetry.
Received: October 10, 2014; in final form March 30, 2015; Published online April 17, 2015
Citation:
Marek Grochowski, Ben Warhurst, “Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds”, SIGMA, 11 (2015), 031, 23 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1012 https://www.mathnet.ru/eng/sigma/v11/p31
|
Statistics & downloads: |
Abstract page: | 593 | Full-text PDF : | 40 | References: | 28 |
|