tag:blogger.com,1999:blog-2748277209726133554.post8156008264829368544..comments2023-10-25T05:08:47.993-07:00Comments on The Language of Bad Physics: Bad Language: “Riemannian Manifold”S.C. Kavassalishttp://www.blogger.com/profile/01326429306907885422noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-2748277209726133554.post-53905450171959268492009-12-30T23:34:15.465-08:002009-12-30T23:34:15.465-08:00In Riemannian geometry, a Riemannian manifold or R...In Riemannian geometry, a Riemannian manifold or Riemannian space (M,g) is a real differentiable manifold M in which each tangent space is equipped with an inner product g, a Riemannian metric, in a manner which varies smoothly from point to point. The metric g is a positive definite symmetric tensor: a metric tensor. This allows one to define various notions such as angles, lengths of curves, areas (or volumes), curvature, gradients of functions and divergence of vector fields. In other words, a Riemannian manifold is a differentiable manifold in which the tangent space at each point is a finite-dimensional Euclidean space. The terms are named after German mathematician Bernhard Riemann. I am a college sophomore with a dual major in Physics and Mathematics @ University of California, Santa Barbara. By the way, i came across these excellent <a href="http://www.funnelbrain.com/" rel="nofollow">physics flash cards</a>. Its also a great initiative by the FunnelBrain team. Amazing!!Anonymousnoreply@blogger.com