## Missouri Journal of Mathematical Sciences

### Invariant Properties of Curves in the Taxicab Geometry

#### Abstract

Let $E^{2}_{T}$ be the group of all isometries of the $2$-dimensional taxicab space $R^{2}_{T}$. For the taxicab group $E^{2}_{T}$, the taxicab type of curves is introduced. All possible taxicab types are found. For every taxicab type, an invariant parametrization of a curve is described. The $E^{2}_{T}$-equivalence of curves is reduced to the problem of the $E^{2}_{T}$-equivalence of paths.

#### Article information

Source
Missouri J. Math. Sci., Volume 26, Issue 2 (2014), 107-114.

Dates
First available in Project Euclid: 18 December 2014

https://projecteuclid.org/euclid.mjms/1418931952

Digital Object Identifier
doi:10.35834/mjms/1418931952

Mathematical Reviews number (MathSciNet)
MR3293808

Zentralblatt MATH identifier
1311.51010

#### Citation

Oren, Idris; Coban, H. Anil. Invariant Properties of Curves in the Taxicab Geometry. Missouri J. Math. Sci. 26 (2014), no. 2, 107--114. doi:10.35834/mjms/1418931952. https://projecteuclid.org/euclid.mjms/1418931952

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