Conformal Deformations of Surfaces and Their Effects on Connections and Geodesics

Authors

  • M. Khalifa Saad Department of Mathematics, Faculty of Science, Islamic University of Madinah, Saudi Arabia
  • Salah G. Elgendi Department of Mathematics, Faculty of Science, Benha University, Benha, EGYPT
  • A. Soleiman $Department of Mathematics, College of Science, Jouf University, Skaka, KSA
  • Hijaz Ahmad Korea University
  • Dragan Pamucar Szechenyi Istvan University, Gyor, Hungary

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.6942

Keywords:

conformal change, Christoffel symbols, covariant derivative, geodesic equation

Abstract

This paper  focuses on the effects of conformal changes on the first fundamental form, with particular emphasis on the transformation of Christoffel symbols, Gaussian curvature, covariant derivatives, and geodesic equations. We study  how conformal scaling alters the connection and curvature properties of surfaces, influencing the intrinsic geometry without changing the underlying conformal class. Special attention is given to how the geodesic flow and curvature expressions adapt under conformal deformation, providing insight into the interplay between local geometry and the metric scaling. Classical results and examples are used to illustrate the impact of conformal metrics on these fundamental geometric quantities.

References

Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Differential Geometry

License

Copyright (c) 2026 M. Khalifa Saad, Salah G. Elgendi, A. Soleiman, Hijaz Ahmad, Dragan Pamucar

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Conformal Deformations of Surfaces and Their Effects on Connections and Geodesics. (2026). European Journal of Pure and Applied Mathematics, 19(2), 6942. https://doi.org/10.29020/nybg.ejpam.v19i2.6942