Missouri Journal of Mathematical Sciences

Invariant Properties of Curves in the Taxicab Geometry

Idris Oren and H. Anil Coban

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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

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1418931952

Digital Object Identifier
doi:10.35834/mjms/1418931952

Mathematical Reviews number (MathSciNet)
MR3293808

Zentralblatt MATH identifier
1311.51010

Subjects
Primary: 51K05: General theory 51K99: None of the above, but in this section 51N30: Geometry of classical groups [See also 20Gxx, 14L35] 51F20: Congruence and orthogonality [See also 20H05]
Secondary: 53A55: Differential invariants (local theory), geometric objects 53A35: Non-Euclidean differential geometry

Keywords
Curve Taxicab geometry Invariant parametrization

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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