RIEMANNIAN GEOMETRY AND ITS APPLICATIONS IN MODERN SCIENCE AND TECHNOLOGY
Keywords:
Riemannian Geometry, Differential Geometry, Riemannian ManifoldAbstract
Riemannian geometry, a branch of differential geometry, investigates smooth manifolds with Riemannian metrics, providing a foundation for understanding curvature and distance in non-Euclidean spaces. This article presents an overview of Riemannian geometry, its mathematical structures, and its pivotal role in various modern applications, including general relativity, robotics, machine learning, and medical imaging. The study highlights the intrinsic geometry of manifolds and emphasizes how Riemannian tools enable deeper exploration in both theoretical and applied sciences.
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