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SIGMA, 2015, Volume 11, 031, 23 pp. (Mi sigma1012)  

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.

DOI: https://doi.org/10.3842/SIGMA.2015.031

Full text: PDF file (439 kB)
Full text: http://www.emis.de/journals/SIGMA/2015/031/
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ArXiv: 1312.4581
MSC: 53B30; 53A55; 34C14
Received: October 10, 2014; in final form March 30, 2015; Published online April 17, 2015
Language:

Citation: Marek Grochowski, Ben Warhurst, “Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds”, SIGMA, 11 (2015), 031, 23 pp.

Citation in format AMSBIB
\Bibitem{GroWar15}
\by Marek~Grochowski, Ben~Warhurst
\paper Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds
\jour SIGMA
\yr 2015
\vol 11
\papernumber 031
\totalpages 23
\mathnet{http://mi.mathnet.ru/sigma1012}
\crossref{https://doi.org/10.3842/SIGMA.2015.031}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3336936}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000352987400001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84929431325}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Grochowski M., Medvedev A., Warhurst B., “3-dimensional left-invariant sub-Lorentzian contact structures”, Differ. Geom. Appl., 49 (2016), 142–166  crossref  mathscinet  zmath  isi  elib  scopus
    2. M. Grochowski, W. Krynski, “On contact sub-pseudo-Riemannian isometries”, ESAIM-Control Optim. Calc. Var., 23:4 (2017), 1751–1765  crossref  mathscinet  zmath  isi
    3. M. Grochowski, B. Warhurst, “Isometries of sub-Riemannian metrics supported on Martinet type distributions”, J. Lie Theory, 28:3 (2018), 767–780  mathscinet  zmath  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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