connection

1. B What is the connection between x^2 and a square shape?

Hello. The curve y = x2 is a parabola that looks like this: I have a shape Square that looks like this: What I am noticing is that if I consider the equation y = x2 and also the shape Square, I find that there is no connection between them but the equation y = x2 is pronounced as x-square...
2. A Is the Berry connection a Levi-Civita connection?

Hello! I have learned Riemannian Geometry, so the only connection I have ever worked with is the Levi-Civita connection(covariant derivative of metric tensor vanishes and the Chrystoffel symbols are symmetric). When performing a parallel transport with the L-C connection, angles and lengths are...
3. A Can you give an example of a non-Levi Civita connection?

Hello!! Since connections in general do not require that we have a Riemannian manifold, but only a smooth manifold, I find it kind of weird that the only examples of connections that I find in the internet are those which use the Levi-Civita connection. So, I wanted to know of any examples of...
4. I Understanding Parallel Transport

I'm currently in a GR class and have come across the notion of parallel transport, and I've searched and searched the last few days to try and understand it but I just can't seem to wrap my head around it, so I'm hoping someone here can clarify for me. The way I picture parallel transport is...
5. Showing that Metric Connections transform as a Connection

1. Homework Statement Show that the metric connection transforms like a connection 2. Homework Equations The metric connection is Γ^{a}_{bc} = \frac{1}{2} g^{ad} ( ∂_{b} g_{dc} + ∂_{c} g_{db} - ∂_{d} g_{bc} ) And of course, in the context of Einstein's GR, we have a symmetric connection...
6. A Question of Cartan's structure equation (in Principal bundle)

I have question about the proof of Cartan's structure equation in the context of pincipal bundle in Nakahara's book. The attached image is taken from the book. To show that the curvature two-form $\Omega$ satisfies $\Omega (X,Y) = {d_P}\omega (X,Y) + [\omega (X),\omega (Y)]$ The author...

12. Non-affine Connections

"Everyone" knows what an affine connection on a smooth manifold is a.k.a. covariant derivative. My questions are: i) Why are those connections called affine? ii) Is there a mathematical object that 'connects neighboring tangent spaces', that could be termed a 'non-affine connection'?
13. Challenge Connecting Multiple Smartphone Mic's Simply & Quickly

Dear Readers, I'm facing a pretty interesting challenge, which is: "How to connect multiple smartphone mic's in the quickest and simplest way?" Here is a use case. I go into a meeting with a group of random (strangers) that all have smartphones, Android, iOS, Windows. Now I want to record this...