Tensors in Differential Geometry

Creative Commons License Clayton Shonkwiler

SLIDES Tensors in Differential Geometry

Speaker: Clayton Shonkwiler, CSU

Abstract: I will give an introduction to the fundamental role played by tensors in differential geometry, with particular emphasis on the idea of a tensor as a multilinear map. This will include brief cameos by some of the most important tensors in geometry: vector fields, differential forms, Riemannian metrics, and the Riemann and Ricci curvature tensors. Time allowing, I will also present an intriguing tensorial connnection between Plucker coordinates on Grassmann manifolds and projection matrices; this last is joint work with Harrison Chapman.

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