On Some Role of Riemannian Geometry
Makur Makuac Chinor *
School of Mathematics, University of Juba, B.O. Box 82 Juba, Central Equaturia, South Sudan.
Mohamed Y. A. Bakhet
School of Mathematics, University of Juba, B.O. Box 82 Juba, Central Equaturia, South Sudan.
Abdelmajid Ali Dafallah
Department of Mathematics, Faculty of Petroleum and Hydrology Engineering, Alsalam University, Almugled, Sudan.
*Author to whom correspondence should be addressed.
Abstract
This paper examines the mathematical significance of Riemannian geometry, including surfaces, Riemannian curvature, Gauss curvature, manifolds, geodesics, and the relationships between them. It also explores the applications of Riemannian geometry in various concepts.
Keywords: Topological manifolds, Riemannian geometry, Riemannian curvature, Gauss curvature, Riemannian manifolds, Lie Algebra, Geodesics