Some results on the geometry of Minkowski plane
Archivum Mathematicum (2010)
- Volume: 046, Issue: 3, page 177-184
- ISSN: 0044-8753
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topWu, Bing Ye. "Some results on the geometry of Minkowski plane." Archivum Mathematicum 046.3 (2010): 177-184. <http://eudml.org/doc/116481>.
@article{Wu2010,
abstract = {In this paper we study the geometry of Minkowski plane and obtain some results. We focus on the curve theory in Minkowski plane and prove that the total curvature of any simple closed curve equals to the total Landsberg angle. As the result, the sum of oriented exterior Landsberg angles of any polygon is also equal to the total Landsberg angle, and when the Minkowski plane is reversible, the sum of interior Landsberg angles of any $n$-gon is $\frac\{n-2\}\{2\}$ times of the total Landsberg angle. Our results generalizes the classical results in plane geometry. We also obtain a new characterizations of Euclidean plane among Minkowski planes.},
author = {Wu, Bing Ye},
journal = {Archivum Mathematicum},
keywords = {Minkowski plane; polar expression; Landsberg angle; Frenet frame; Minkowski plane; polar expression; Landsberg angle; Frenet frame},
language = {eng},
number = {3},
pages = {177-184},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some results on the geometry of Minkowski plane},
url = {http://eudml.org/doc/116481},
volume = {046},
year = {2010},
}
TY - JOUR
AU - Wu, Bing Ye
TI - Some results on the geometry of Minkowski plane
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 3
SP - 177
EP - 184
AB - In this paper we study the geometry of Minkowski plane and obtain some results. We focus on the curve theory in Minkowski plane and prove that the total curvature of any simple closed curve equals to the total Landsberg angle. As the result, the sum of oriented exterior Landsberg angles of any polygon is also equal to the total Landsberg angle, and when the Minkowski plane is reversible, the sum of interior Landsberg angles of any $n$-gon is $\frac{n-2}{2}$ times of the total Landsberg angle. Our results generalizes the classical results in plane geometry. We also obtain a new characterizations of Euclidean plane among Minkowski planes.
LA - eng
KW - Minkowski plane; polar expression; Landsberg angle; Frenet frame; Minkowski plane; polar expression; Landsberg angle; Frenet frame
UR - http://eudml.org/doc/116481
ER -
References
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- Shen, Z., Lectures on Finsler Geometry, World Sci., Singapore, 2001. (2001) Zbl0974.53002MR1845637
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