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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. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
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Mathematical Citation Quotient (MCQ) 2018: 0.53

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Three-dimensional connected groups of automorphisms of toroidal circle planes

Brendan Creutz / Duy Ho / Günter F. Steinke
Published Online: 2019-09-11 | DOI: https://doi.org/10.1515/advgeom-2019-0031

Abstract

We contribute to the classification of toroidal circle planes and flat Minkowski planes possessing three-dimensional connected groups of automorphisms. When such a group is an almost simple Lie group, we show that it is isomorphic to PSL(2, ℝ). Using this result, we describe a framework for the full classification based on the action of the group on the point set.

Keywords: Circle plane; Minkowski plane; automorphism group

MSC 2010: 51H15; 51B20

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About the article

Received: 2018-09-14

Revised: 2018-12-27

Published Online: 2019-09-11


Communicated by: R. Löwen

Funding: The second author was supported by a University of Canterbury Doctoral Scholarship.


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2019-0031.

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