On (m̄,m)-Conformal Mappings

Randjelović, Branislav M.; Simjanović, Dušan J.; Vesić, Nenad O.; Djurišić, Ivana; Vlahović, Branislav D.

doi:10.3390/axioms14090652

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On (m̄,m)-Conformal Mappings

by

Branislav M. Randjelović

^1,2,*

,

Dušan J. Simjanović

³

,

Nenad O. Vesić

⁴

,

Ivana Djurišić

⁵

and

Branislav D. Vlahović

⁶

¹

Faculty of Electronic Engineering, University of Niš, 18000 Niš, Serbia

²

Faculty of Teachers Education, University of K. Mitrovica, 38218 Leposavić, Serbia

³

Faculty of Information Technology, Belgrade Metropolitan University, 11000 Belgrade, Serbia

⁴

Mathematical Institute of Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia

⁵

Institute for Multidisciplinary Research, University of Belgrade, 11000 Belgrade, Serbia

⁶

Department of Physics, North Carolina Central University, Durham, NC 27707, USA

^*

Author to whom correspondence should be addressed.

Axioms 2025, 14(9), 652; https://doi.org/10.3390/axioms14090652

Submission received: 27 July 2025 / Revised: 18 August 2025 / Accepted: 20 August 2025 / Published: 22 August 2025

(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)

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Abstract

Conformal mappings between Riemannian spaces

{\bar{R}}_{N}

and

R_{N}

are defined by the explicit transformation of the metric tensor of the space

{\bar{R}}_{N}

to the metric tensor of the space

R_{N}

. Geodesic mapping between these two Riemannian spaces is a transformation that transforms any geodesic line of the space

{\bar{R}}_{N}

to a geodesic line of the space

R_{N}

. In this research, we defined an m-conformal line of a Riemannian space, which is geodesic if

m = 0

. Based on this definition, we involved the concept of

(\bar{m}, m)

-conformal mapping as a transformation

{\bar{R}}_{N} \to R_{N}

in which any

\bar{m}

-conformal line of the space

{\bar{R}}_{N}

transforms to an m-conformal line of the space

R_{N}

. The result of this research is the establishment of three invariants for these mappings. At the end of this research, we gave an example of a scalar geometrical object which may be used in physics.

Keywords: mapping; Riemannian space; invariant; variation

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MDPI and ACS Style

Randjelović, B.M.; Simjanović, D.J.; Vesić, N.O.; Djurišić, I.; Vlahović, B.D. On (m̄,m)-Conformal Mappings. Axioms 2025, 14, 652. https://doi.org/10.3390/axioms14090652

AMA Style

Randjelović BM, Simjanović DJ, Vesić NO, Djurišić I, Vlahović BD. On (m̄,m)-Conformal Mappings. Axioms. 2025; 14(9):652. https://doi.org/10.3390/axioms14090652

Chicago/Turabian Style

Randjelović, Branislav M., Dušan J. Simjanović, Nenad O. Vesić, Ivana Djurišić, and Branislav D. Vlahović. 2025. "On (m̄,m)-Conformal Mappings" Axioms 14, no. 9: 652. https://doi.org/10.3390/axioms14090652

APA Style

Randjelović, B. M., Simjanović, D. J., Vesić, N. O., Djurišić, I., & Vlahović, B. D. (2025). On (m̄,m)-Conformal Mappings. Axioms, 14(9), 652. https://doi.org/10.3390/axioms14090652

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