Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 4

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

Sayfa
1110–1120
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 $\mathbb{R}_{\infty}^3$.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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 $\mathbb{R}_{\infty}^3$.
📊
Temel Bulgular & Veri: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 $\mathbb{R}_{\infty}^3$.
💡
Sonuç & Katkı: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 $\mathbb{R}_{\infty}^3$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:geodesic · sector · plane

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 $\mathbb{R}_{\infty}^3$.

🔖

Bu Makaleye Atıf Yap

KILIÇ, M. (2022). Isometry classes of planes in $(\mathbb{R}^3,d_{\infty})$. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 4, 1110–1120. https://ajindex.com/articles/529781

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (8)

  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.