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kostja

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Okay, I edited the above file a little b...

kostja 46
September 18 2011
0 0

Okay, I edited the above file a little bit and removed some bugs. I tested the new function

SecondFundamentalForm

for S^1 in IR^2 and for S^2 in IR^3. And the results seem to be consistent.

Fell free to use it, in this case please report bugs or post even bugfixes here.

Also, feel free to ask questions about the methods.

Kind regards

Konstantin

 

EDIT: new version: tangentbundle.mw

Okay, I edited the above file a little b...

kostja 46
September 18 2011

Okay, I edited the above file a little bit and removed some bugs. I tested the new function

SecondFundamentalForm

for S^1 in IR^2 and for S^2 in IR^3. And the results seem to be consistent.

Fell free to use it, in this case please report bugs or post even bugfixes here.

Also, feel free to ask questions about the methods.

Kind regards

Konstantin

 

EDIT: new version: tangentbundle.mw

Not quite what I wanted to do......

kostja 46
September 18 2011
0 0

Hi!

Thank you for your suggestions. I didn't looked into the PullbackVector method, because I thought I need a diffeomorphism to be able to pull back vectors (in differential geometry you, do: f^* X = f_*^(-1) X ° f).

It's also not quite what I want to do, if I would be able to find a right inverse for the imbedding map. Because in the end, I would get a vectorfiled on M, and not on S, what I'm looking for.

I have tried to construct the pulled back bundle and to pull back the connection from M to it. Maybe you can help me with it. There's a little failure in it, I can't figure out. (See my anwser on the question please.)

 

Kind regards
Konstantin

Not quite what I wanted to do......

kostja 46
September 18 2011

Hi!

Thank you for your suggestions. I didn't looked into the PullbackVector method, because I thought I need a diffeomorphism to be able to pull back vectors (in differential geometry you, do: f^* X = f_*^(-1) X ° f).

It's also not quite what I want to do, if I would be able to find a right inverse for the imbedding map. Because in the end, I would get a vectorfiled on M, and not on S, what I'm looking for.

I have tried to construct the pulled back bundle and to pull back the connection from M to it. Maybe you can help me with it. There's a little failure in it, I can't figure out. (See my anwser on the question please.)

 

Kind regards
Konstantin

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