bio | website | |
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location | Los Angeles | |
age | ||
visits | member for | 3 years |
seen | Apr 21 at 0:40 | |
stats | profile views | 174 |
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 $N$? |