| Title:
|
Some results on the geometry of Minkowski plane (English) |
| Author:
|
Wu, Bing Ye |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
177-184 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Minkowski plane |
| Keyword:
|
polar expression |
| Keyword:
|
Landsberg angle |
| Keyword:
|
Frenet frame |
| MSC:
|
53B40 |
| MSC:
|
53C60 |
| idZBL:
|
Zbl 1240.53132 |
| idMR:
|
MR2735904 |
| . |
| Date available:
|
2010-10-22T05:34:10Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140786 |
| . |
| Reference:
|
[1] Bao, D., Lackey, B.: Randers surfaces whose Laplacians have completely positive symbol.Nonlinear Anal. 38 (1999), 27–40. Zbl 0945.53045, MR 1692941 |
| Reference:
|
[2] Bao, D., Shen, Z.: In the volume of unit tangent spheres in a Finsler manifold.Results Math. 26 (1994), 1–17. MR 1290676, 10.1007/BF03322283 |
| Reference:
|
[3] Deiche, A.: Über die Finsler-Räume mit $A_i=0$.Arch. Math. (Basel) 4 (1953), 45–51. MR 0055026, 10.1007/BF01899750 |
| Reference:
|
[4] Rademacher, H. B.: A sphere theorem for non-reversible Finsler metrics.Math. Ann. 328 (2004), 373–387. Zbl 1050.53063, MR 2036326, 10.1007/s00208-003-0485-y |
| Reference:
|
[5] Shen, Z.: Lectures on Finsler Geometry.World Sci., Singapore, 2001. Zbl 0974.53002, MR 1845637 |
| . |
