Abstract
Euclidean geometry is the only Minkowski geometry in which either there is a centrally symmetric, or a quadratic conic, or there is a conical ellipsoid or hyperboloid.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Busemann, H., Kelly, P.J.: Projective Geometries and Projective Metrics. Academic Press, New York (1953)
Busemann, H.: The Geometry of Geodesics. Academic Press, New York (1955)
Cheng, S.S., Li, W.: Analytic Solutions of Functional Equations. World Scientific, New Jersey (2008)
Ghandehari, M.A.: Heron’s problem in the Minkowski plane. Technical Report of Department of Mathematics at the University of Texas at Arlington, vol. 306. http://hdl.handle.net/10106/2500 (1997)
Horváth, Á.G., Martini, H.: Conics in normed planes. Extracta Math. 26(1), 29–43. arXiv:1102.3008 (2011)
Tamássy, L., Bélteky, K.: On the coincidence of two kinds of ellipses in Minkowskian and Finsler planes. Publ. Math. Debr. 31(3–4), 157–161 (1984)
Tamássy, L., Bélteky, K.: On the coincidence of two kinds of ellipses in Riemannian and in Finsler spaces. Coll. Math. Soc. J. Bolyai 46, 1193–1200 (1988)
https://en.wikipedia.org/wiki/Ellipse. Accessed 6 Aug 2017
Acknowledgements
The author is grateful to József Kozma for discussing some parts of this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by NFSR of Hungary (OTKA), Grant Number K 116451.
Rights and permissions
About this article
Cite this article
Kurusa, Á. Conics in Minkowski geometries. Aequat. Math. 92, 949–961 (2018). https://doi.org/10.1007/s00010-018-0592-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-018-0592-1