Transformation group in moving frame method
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I am reading the following paper: https://ieeexplore.ieee.org/document/4700863/ (just at the beginning of Section II-B)
My questions are the following:
- What is $partial_gphi_g$ ? (partial differentiation of a diffeomorphism $phi_g$ w.r.t one group element $g$? )
- Why did that paper choose $(e,xi^0)$, can we choose $(g,xi^0)$ with $gin G$?
- Can $phi_g^a$ be viewed as a matrix? (since the paper says $phi_g^a$ is invertible).
- If 3. is yes, then the paper also says $(phi^a_g,phi^b_g)$ has $r$ and $n-r$ components, what do components here mean? different sub-block of a big matrix?
I think 2. is related to tangent space of a diffeomorphism; however, I still want to get a more complete information.
Thanks!
differential-geometry lie-groups coordinate-systems
asked Aug 26 at 6:22
sleeve chen
2,79931646
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up vote
1
down vote
favorite
I am reading the following paper: https://ieeexplore.ieee.org/document/4700863/ (just at the beginning of Section II-B)
My questions are the following:
- What is $partial_gphi_g$ ? (partial differentiation of a diffeomorphism $phi_g$ w.r.t one group element $g$? )
- Why did that paper choose $(e,xi^0)$, can we choose $(g,xi^0)$ with $gin G$?
- Can $phi_g^a$ be viewed as a matrix? (since the paper says $phi_g^a$ is invertible).
- If 3. is yes, then the paper also says $(phi^a_g,phi^b_g)$ has $r$ and $n-r$ components, what do components here mean? different sub-block of a big matrix?
I think 2. is related to tangent space of a diffeomorphism; however, I still want to get a more complete information.
Thanks!
differential-geometry lie-groups coordinate-systems
asked Aug 26 at 6:22
sleeve chen
2,79931646
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am reading the following paper: https://ieeexplore.ieee.org/document/4700863/ (just at the beginning of Section II-B)
My questions are the following:
- What is $partial_gphi_g$ ? (partial differentiation of a diffeomorphism $phi_g$ w.r.t one group element $g$? )
- Why did that paper choose $(e,xi^0)$, can we choose $(g,xi^0)$ with $gin G$?
- Can $phi_g^a$ be viewed as a matrix? (since the paper says $phi_g^a$ is invertible).
- If 3. is yes, then the paper also says $(phi^a_g,phi^b_g)$ has $r$ and $n-r$ components, what do components here mean? different sub-block of a big matrix?
I think 2. is related to tangent space of a diffeomorphism; however, I still want to get a more complete information.
Thanks!
differential-geometry lie-groups coordinate-systems
asked Aug 26 at 6:22
sleeve chen
2,79931646
I am reading the following paper: https://ieeexplore.ieee.org/document/4700863/ (just at the beginning of Section II-B)
My questions are the following:
- What is $partial_gphi_g$ ? (partial differentiation of a diffeomorphism $phi_g$ w.r.t one group element $g$? )
- Why did that paper choose $(e,xi^0)$, can we choose $(g,xi^0)$ with $gin G$?
- Can $phi_g^a$ be viewed as a matrix? (since the paper says $phi_g^a$ is invertible).
- If 3. is yes, then the paper also says $(phi^a_g,phi^b_g)$ has $r$ and $n-r$ components, what do components here mean? different sub-block of a big matrix?
I think 2. is related to tangent space of a diffeomorphism; however, I still want to get a more complete information.
Thanks!
differential-geometry lie-groups coordinate-systems
asked Aug 26 at 6:22
sleeve chen
2,79931646
asked Aug 26 at 6:22
sleeve chen
2,79931646
asked Aug 26 at 6:22
sleeve chen
2,79931646
asked Aug 26 at 6:22
sleeve chen
2,79931646
2,79931646
add a comment |Â
add a comment |Â
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