kostja

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12 years, 335 days

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These are replies submitted by kostja

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 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

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

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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