Tensor Calculus Ep. 15 | Riemann Curvature Tensor
Channel: Andrew Dotson
Category: Education
Tags: odufield equationsriccidegreegradschoolderivativegeneral relativitygrtensorcalculusphdandrewcurvaturecovariantcommutatornmsuparallel transportmajorphysicsgradstudentriemanneinsteindotsonchristoffel
Description: Todays episode explores the concept of curvature, and we finally arrive at the Riemann Curvature Tensor. Eigenchris's video: youtube.com/watch?v=-Il2FrmJtcQ&t=1364s&ab_channel=eigenchris This series is based off of the book "Tensor Calculus for Physics" by Dwight Neuenschwander amazon.com/gp/product/1421415658/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=1421415658&linkCode=as2&tag=andrewdotson-20&linkId=b45243268a957a6cfdfc854a8f677a58 0:00 Introduction 1:45 Extrinsic/Intrinsic Curvature 6:32 Parallel Transporting Vector 11:32 Derivatives as Generators of Translation 14:50 Commutator of Covariant Derivatives 32:46 The Riemann Curvature Tensor 35:49 RCT Analogy to Intro Calculus 37:08 Do Cylinders have Intrinsic Curvature 38:24 2-D Sphere vs 3-D Euclidian Metric in Spherical Coordinates 40:25 Next Videos and Conclusion
