Tensors in Differential Geometry, Clayton Shonkwiler

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.

Видео Tensors in Differential Geometry, Clayton Shonkwiler канала James Wilson