The Best Metric on a Sphere
May 6, 2014
Bailey Hall 207
Refreshments will be served in Bailey Hall 204 4:45pm
We will take a closer look at the natural geometry of the sphere. Then we introduce an entire family of possible geometries (or “Riemannian metrics’’) on the sphere. Among these we seek the "best one" by formulating an appropriate version of Calabi’s Extremal Kaehler metrics. The answer will not really be a big surprise, but I hope that this simple example can illustrate a key question often asked in differential geometry. We will use the notion of arc length of parametrized curves as defined in MTH 115 (IMP) and we will use the idea of parametrized surfaces as introduced in MTH 117 (IMP). We also need to use the Chain Rule from MTH 115.
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