Rachelle DeCoste-West Point
Geodesics of some familiar manifolds
Let us define a manifold to be any abstract surface of arbitrary dimension.
Then we can ask the question, “what is the shortest path between any two points
on a manifold?” This question leads us to define geodesics on Riemannian
manifolds as locally shortest curves. In this talk we will look at some familiar
surfaces, such as the plane and the sphere, and explore their geodesic
properties. We will also consider geodesics on some possibly less familiar
manifolds, including the torus and a subspace of matrices. Finally, we will give
an indication of the current research being done to describe geodesic properties
on more complicated manifolds.
This talk is sponsored by the Marist College Mathematics Club
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