Some results on the geometry of Minkowski plane

Bing Ye Wu

Address: Department of Mathematics, Minjiang University, Fuzhou, Fujiang, 350108, China


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.

AMSclassification: primary 53C60; secondary 53B40.

Keywords: Minkowski plane, polar expression, Landsberg angle, Frenet frame.