197 reputation
6
bio website
location Los Angeles
age
visits member for 3 years
seen Apr 21 at 0:40
University lecturer.

Feb
8
comment Injectivity of Lie group exponential function
If you give your Lie group a metric then the exponential will be injective outside the tangential cut locus. These have been calculated for the matrix Lie groups by Sakai. I think it should be rather straightforward to see what's going on in the case of $U(2)$.
Feb
7
comment Grassmannian frames in the Grassmannian
Take a look at the paper by Joel Rouyer entitled "On $p$-tuples of the Grassmann manifolds"; it looks relevant.
Feb
7
revised Connections on a Lie Group
Improve formatting
Feb
5
comment Connections on a Lie Group
@José You can ignore the reference to the Levi-Civita connection because it's not relevant to my question. Simply put, I'm asking what connections on a Lie group are canonical w.r.t. some reductive decomposition.
Feb
5
revised Connections on a Lie Group
Improving format
Feb
5
comment Connections on a Lie Group
@QiaochuYuan Could you elaborate?
Feb
5
asked Connections on a Lie Group
Aug
17
comment Stiefel manifolds and polar decompositions
@Fran: I'm not sure of the correct terminology here. I've changed Cartan to polar.
Aug
17
revised Stiefel manifolds and polar decompositions
edited title
Aug
17
revised Stiefel manifolds and polar decompositions
added 44 characters in body; edited title
Aug
16
revised Stiefel manifolds and polar decompositions
deleted 4 characters in body
Aug
16
revised Stiefel manifolds and polar decompositions
added 12 characters in body
Aug
15
asked Stiefel manifolds and polar decompositions
Jul
18
comment Torsion and submanifolds
@Ramiro: Since people want to vote the question down, how do I go about modifying it? It's not a big change by the way.
Jul
18
revised Torsion and submanifolds
Modification of question.
Jul
18
comment Torsion and submanifolds
@Robert: I meant for the expression $\nabla_XY-\nabla_YX$ to be evaluated at a point in the submaniofld.
Jul
18
comment Torsion and submanifolds
@Peter: So it's the Lie bracket that respects vectors tangent to $N$. Thanks, that clears things up.
Jul
18
accepted Torsion and submanifolds
Jul
18
comment Torsion and submanifolds
@Mariano: Good point! But what about the term $\nabla_XY-\nabla_YX$?
Jul
18
comment Torsion and submanifolds
@Robert: Is it the case that $\nabla_XY-\nabla_YX$ lies in the tangent space of $N$?