Research Article
BibTex RIS Cite
Year 2019, Volume: 48 Issue: 4, 1110 - 1120, 08.08.2019

Abstract

References

  • [1] N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6, 405–439, 1956.
  • [2] M.R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999.
  • [3] D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics American Mathematical Society, USA, 2001.
  • [4] M. Kılıç and S. Koçak, Tight Span of Subsets of The Plane With The Maximum Metric, Adv. Math. 301, 693–710, 2016.
  • [5] A. Moezzi, The Injective Hull of Hyperbolic Groups, Dissertation ETH Zurich, No: 18860, 2010.
  • [6] L. Nachbin, A Theorem of The Hahn-Banach Type For Linear Transformations, Trans. Amer. Math. Soc. 68, 28–46, 1950.
  • [7] A. Papadopoulos, Metric Spaces, Convexity and Nonpositive Curvature, IRMA Lect. Math. Theor. Phys. European Mathematical Society, Germany, 2005.
  • [8] M. Pavon, Injective Convex Polyhedra, Discrete Comput. Geom. doi:10.1007/s00454- 016-9810-6, 2016.

Isometry classes of planes in $(\mathbb{R}^3,d_{\infty})$

Year 2019, Volume: 48 Issue: 4, 1110 - 1120, 08.08.2019

Abstract

We determine geodesics in $\mathbb{R}_{\infty}^n$ (i.e. $(\mathbb{R}^n,d_{\infty})$) and by using this, classify planes up to isometry in $\mathbb{R}_{\infty}^3$.

References

  • [1] N. Aronszajn and P. Panitchpakdi, Extension of uniformly continuous transformations and hyperconvex metric spaces, Pacific J. Math. 6, 405–439, 1956.
  • [2] M.R. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Grundlehren der mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999.
  • [3] D. Burago, Y. Burago and S. Ivanov, A Course in Metric Geometry, Graduate Studies in Mathematics American Mathematical Society, USA, 2001.
  • [4] M. Kılıç and S. Koçak, Tight Span of Subsets of The Plane With The Maximum Metric, Adv. Math. 301, 693–710, 2016.
  • [5] A. Moezzi, The Injective Hull of Hyperbolic Groups, Dissertation ETH Zurich, No: 18860, 2010.
  • [6] L. Nachbin, A Theorem of The Hahn-Banach Type For Linear Transformations, Trans. Amer. Math. Soc. 68, 28–46, 1950.
  • [7] A. Papadopoulos, Metric Spaces, Convexity and Nonpositive Curvature, IRMA Lect. Math. Theor. Phys. European Mathematical Society, Germany, 2005.
  • [8] M. Pavon, Injective Convex Polyhedra, Discrete Comput. Geom. doi:10.1007/s00454- 016-9810-6, 2016.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Mehmet Kılıç 0000-0003-3713-5470

Publication Date August 8, 2019
Published in Issue Year 2019 Volume: 48 Issue: 4

Cite

APA Kılıç, M. (2019). Isometry classes of planes in $(\mathbb{R}^3,d_{\infty})$. Hacettepe Journal of Mathematics and Statistics, 48(4), 1110-1120.
AMA Kılıç M. Isometry classes of planes in $(\mathbb{R}^3,d_{\infty})$. Hacettepe Journal of Mathematics and Statistics. August 2019;48(4):1110-1120.
Chicago Kılıç, Mehmet. “Isometry Classes of Planes in $(\mathbb{R}^3,d_{\infty})$”. Hacettepe Journal of Mathematics and Statistics 48, no. 4 (August 2019): 1110-20.
EndNote Kılıç M (August 1, 2019) Isometry classes of planes in $(\mathbb{R}^3,d_{\infty})$. Hacettepe Journal of Mathematics and Statistics 48 4 1110–1120.
IEEE M. Kılıç, “Isometry classes of planes in $(\mathbb{R}^3,d_{\infty})$”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, pp. 1110–1120, 2019.
ISNAD Kılıç, Mehmet. “Isometry Classes of Planes in $(\mathbb{R}^3,d_{\infty})$”. Hacettepe Journal of Mathematics and Statistics 48/4 (August 2019), 1110-1120.
JAMA Kılıç M. Isometry classes of planes in $(\mathbb{R}^3,d_{\infty})$. Hacettepe Journal of Mathematics and Statistics. 2019;48:1110–1120.
MLA Kılıç, Mehmet. “Isometry Classes of Planes in $(\mathbb{R}^3,d_{\infty})$”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 4, 2019, pp. 1110-2.
Vancouver Kılıç M. Isometry classes of planes in $(\mathbb{R}^3,d_{\infty})$. Hacettepe Journal of Mathematics and Statistics. 2019;48(4):1110-2.