August 22, 2025Open Access

On (m̄,m)-Conformal Mappings

BRBranislav RandjelovićUniversity of Nis DSDušan J. SimjanovićMetropolitan University NVNenad O. VesićSerbian Academy of Sciences and Arts

Key Points

The research establishes three invariants for m-conformal mappings, enhancing understanding of geometric transformations in Riemannian spaces.
Geodesic mapping transforms geodesic lines between Riemannian spaces, helping to understand their geometric properties.
In this work, the concept of m-conformal lines is introduced, revealing their connections to standard geodesics when m is set to zero.
An example of a scalar geometrical object linked to the mappings is provided, showing potential applications in physics.

Abstract

Conformal mappings between Riemannian spaces R¯N and RN are defined by the explicit transformation of the metric tensor of the space R¯N to the metric tensor of the space RN. Geodesic mapping between these two Riemannian spaces is a transformation that transforms any geodesic line of the space R¯N to a geodesic line of the space RN. 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 (m¯,m)-conformal mapping as a transformation R¯N→RN in which any m¯-conformal line of the space R¯N transforms to an m-conformal line of the space RN. 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.

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