lavinia's latest activity

Here is a digram that I got Gemini to make that shows the warping of the 3 ball with a cylindurcal tube through its center removed to...

By the way, here is one of the standard conclusions derived from the non-triviality of the configuration manifold (in this case, SO(3))...

I thought it would be helpful to visualize the attachment of a vector field of index two to a fiber. The whole process can be zoomed in...

RE: post #33: yes, I tried to say something like this in post #10.

In terms of the sequence, SO(2)->SO(3)->S^2, since SO(2) is closed in SO(3) ,this sequence describes a fiber bundle whose fibers are...

This is getting clearer, if slowly. We know every (non trivial) rotation about a given axis, belongs to a circle subgroup of rotations...

Building again on lavinia's posts, we know SO(3) is homeomorphic to RP^3, the real projective 3-space, which is a solid ball with...

I was asking because I wanted to visualize the inability to have a null homotopy. I am thinking of the case of the 3 sphere where all...

Ok. But how does one know that these critical geodesics are not-null homotopic from this?

I was referring to the Maupertuis metric. Let ##x = (x^1, x^2, x^3)## be local coordinates on ##SO(3)##, and let a rigid body with a...

@Matterwave The first description in Post #9 of the tangent circle bundle of the 2 sphere as a circlular stack of of projective planes...

@wrobel can you explain that a little more. I gather that the geodesic here is the full rotation around an axis. And the Riemannian...

I just want to remark that if we think in terms of matrices, then it is obvious just from the definition that SO(3) is a circle bundle...

A full ##2\pi## rotation of a rigid body about a fixed axis forms a non-contractible loop in ##SO(3)##.

yes. The tangent space to the sphere at any point is just a two dimensional plane so the vectors of length 1 in each plane make a circle...