Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

4 Issues per year

IMPACT FACTOR 2016: 0.552

CiteScore 2016: 0.61

SCImago Journal Rank (SJR) 2016: 0.564
Source Normalized Impact per Paper (SNIP) 2016: 1.021

Mathematical Citation Quotient (MCQ) 2016: 0.45

See all formats and pricing
More options …
Ahead of print


Continuous space-time transformations

Clément de Seguins Pazzis
  • Corresponding author
  • Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin-en-Yvelines, 45 avenue des Etats-Unis, 78035 Versailles cedex, France
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Peter Šemrl
Published Online: 2018-04-05 | DOI: https://doi.org/10.1515/advgeom-2017-0056


We prove that every continuous map acting on the four-dimensional Minkowski space and preserving light cones in one direction only is either a Poincaré similarity, that is, a product of a Lorentz transformation and a dilation, or it is of a very special degenerate form.

Keywords: Minkowski space; space-time event; hermitian matrix; coherency; adjacency; homotopy

MSC 2010: 15A86; 55E40; 83A05


  • [1]

    A. D. Aleksandrov, Seminar Report. Uspehi Mat. Nauk. 5 (1950), 187.Google Scholar

  • [2]

    A. D. Alexandrov, A contribution to chronogeometry. Canad. J. Math. 19 (1967), 1119–1128. MR0219018 Zbl 0173.24603CrossrefGoogle Scholar

  • [3]

    A. D. Alexandrov, Mappings of spaces with families of cones and space-time transformations. Ann. Mat. Pura Appl. (4) 103 (1975), 229–257. MR0378695 Zbl 0302.50009CrossrefGoogle Scholar

  • [4]

    W. Benz, Real geometries. Bibliographisches Institut, Mannheim 1994. MR1290992 Zbl 0819.51002Google Scholar

  • [5]

    H. J. Borchers, G. C. Hegerfeldt, The structure of space-time transformations. Comm. Math. Phys. 28 (1972), 259–266. MR0347307 Zbl 0242.53017CrossrefGoogle Scholar

  • [6]

    A. Chubarev, I. Pinelis, Linearity of space-time transformations without the one-to-one, line-onto-line, or constancy-of-speed-of-light assumptions. Comm. Math. Phys. 215 (2000), 433–441. MR1799854 Zbl 0981.51022CrossrefGoogle Scholar

  • [7]

    L. K. Hua, Starting with the unit circle. Springer 1981. MR665916 Zbl 0481.43005Google Scholar

  • [8]

    W.-l. Huang, P. Šemrl, Adjacency preserving maps on Hermitian matrices. Canad. J. Math. 60 (2008), 1050–1066. MR2442047 Zbl 1151.15001CrossrefGoogle Scholar

  • [9]

    J. A. Lester, A physical characterization of conformal transformations of Minkowski spacetime. In: Combinatorics ’81 (Rome, 1981), volume 18 of Ann. Discrete Math., 567–574, North-Holland 1983. MR695841 Zbl 0507.51004Google Scholar

  • [10]

    J. A. Lester, M. A. McKiernan, On null cone preserving mappings. Math. Proc. Cambridge Philos. Soc. 81 (1977), 455–462. MR0475596 Zbl 0358.50002CrossrefGoogle Scholar

  • [11]

    W. F. Pfeffer, Lorentz transformations of a Hilbert space. Amer. J. Math. 103 (1981), 691–709. MR623134 Zbl 0471.46014CrossrefGoogle Scholar

  • [12]

    I. Popovici, D. C. Rădulescu, Characterizing the conformality in a Minkowski space. Ann. Inst. H. Poincaré Sect. A (N.S.) 35 (1981), 131–148. MR637239 Zbl 0476.51014Google Scholar

  • [13]

    E. M. Schröder, Ein einfacher Beweis des Satzes von Alexandroff–Lester. J. Geom. 37 (1990), 153–158. MR1041988 Zbl 0704.51010CrossrefGoogle Scholar

  • [14]

    E. C. Zeeman, Causality implies the Lorentz group. J. Mathematical Phys. 5 (1964), 490–493. MR0162587 Zbl 0133.23205CrossrefGoogle Scholar

About the article

Received: 2016-03-07

Revised: 2016-08-09

Published Online: 2018-04-05

Funding: The second author was supported by a grant from ARRS, Slovenia.

Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0056.

Export Citation

© 2017 Walter de Gruyter GmbH Berlin/Boston. Copyright Clearance Center

Comments (0)

Please log in or register to comment.
Log in