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Abstract:
In a painting done in perspective, every pair of lines, even parallel
lines, intersects at a single point. For example, envision railroad
tracks receding into the distance. This notion of perspective gave
birth to a type of non-Euclidean geometry called projective
geometry. I will discuss a related family of spaces called projective
planes which are of current interest to differential geometers since
they belong to a small class of spaces with certain very nice
symmetries. Specifically, I will discuss natural ways to view
projective planes as Riemannian manifolds and how it is possible to
relate different models of the Cayley projective plane.
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