To illustrate this, consider a simple case: a 2D sphere where we want to find the shortest path between two points. In Riemannian geometry, these are "Great Circles." Why this is helpful:
: It supports modern fields like Geometric Statistics , where Riemannian means are used to analyze data on curved spaces. Riemannian Geometry.pdf
: A visual representation of the resulting manifold and the geodesics (shortest paths) between two user-defined points. Educational Visualization: Geodesic on a Sphere To illustrate this, consider a simple case: a
Introduction to Riemannian Geometry and Geometric Statistics - HAL-Inria To illustrate this
Since the "Riemannian Geometry.pdf" document likely covers the study of differentiable manifolds equipped with an inner product at each point, a highly useful feature for a student or researcher is a .