On affine planes non-extensible to Laguerre planes and some related problems

Krystyna Gozdalska

Mathematica Bohemica (1991)

  • Volume: 116, Issue: 1, page 2-11
  • ISSN: 0862-7959

Abstract

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Some examples of affine planes non-extensible to a Laguerre plane are studied and conditions for the uniqueness of a Laguerre extension are given.

How to cite

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Gozdalska, Krystyna. "On affine planes non-extensible to Laguerre planes and some related problems." Mathematica Bohemica 116.1 (1991): 2-11. <http://eudml.org/doc/29351>.

@article{Gozdalska1991,
abstract = {Some examples of affine planes non-extensible to a Laguerre plane are studied and conditions for the uniqueness of a Laguerre extension are given.},
author = {Gozdalska, Krystyna},
journal = {Mathematica Bohemica},
keywords = {Laguerrian extensions; the Hughes projective plane over nearfield; Laguerrian extension; Hughes projective plane over near-fields},
language = {eng},
number = {1},
pages = {2-11},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On affine planes non-extensible to Laguerre planes and some related problems},
url = {http://eudml.org/doc/29351},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Gozdalska, Krystyna
TI - On affine planes non-extensible to Laguerre planes and some related problems
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 1
SP - 2
EP - 11
AB - Some examples of affine planes non-extensible to a Laguerre plane are studied and conditions for the uniqueness of a Laguerre extension are given.
LA - eng
KW - Laguerrian extensions; the Hughes projective plane over nearfield; Laguerrian extension; Hughes projective plane over near-fields
UR - http://eudml.org/doc/29351
ER -

References

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  1. R. Artzy, 10.1007/BF01949677, Journal of Geometry, 5(2) (1974), 1-8. (1974) Zbl0287.50018MR0380621DOI10.1007/BF01949677
  2. Yi Chen, A characterization of some geometries of chains, Can. J. Math., No. 2, 26 (1974), 258-260. (1974) Zbl0281.50011MR0338919
  3. K. Gozdalska, Zagadnienie rozszerzalności afinicznych struktur incydencyjnych do płaszczyzn Laguerre'a, doctor thesis, Toruń 1985. (1985) 
  4. K. Gozdalska, Affine planes which induce Laguerre planes, Geometria, Scient. Chapt. of Institute of Technology in Poznań, 15 (1986), 99-110. (1986) Zbl0605.51006MR0865126
  5. E. Hartman, 10.1007/BF01988555, Journal of Geometry, 13(1) (1979), 49-67. (1979) MR0547163DOI10.1007/BF01988555
  6. E. Hartman, Moulton-Laguerre-Еbenen, Arch. Math., 17 (1976), 424-435. (1976) MR0420431
  7. D. R. Hughes, A class of non-Desarguesian projective planes, Can. J. Math., No. 3, 9 (1957), 378-388. (1957) Zbl0082.35701MR0087960
  8. J. Hunjic M. Polonijo V. Volenec, Uniqueness of the сompletion of the Еuсlidean plane to a Möbius plane, Glasnik Matematiсki, No. 1, 9 (29) (1974), 125-130. (1974) MR0348625

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