I don't know what else to tell you since you won't show me a worksheet. It could be a trivial kind of error that you are making. For example, are you using the "assuming" facility anywhere?  That can cause problems if used incorrectly.

I don't know what else to tell you since you won't show me a worksheet. It could be a trivial kind of error that you are making. For example, are you using the "assuming" facility anywhere?  That can cause problems if used incorrectly.

I will contact you by email then.

Could you please provide a little more info?

The metric?

A worksheet?

Maple version?

Thanks.

charlie

Does this work in classic mode?

If I can find the time, I will try to write something up with the nice level of clarity that you provided us in your post.  In the meantime, in Maple Help, have a look at what is here

DifferentialGeometry/LessonsAndTutorials/DifferentialGeometry/AdaptedFrames

charlie

Just to clarify something...  In DifferentialGeometry you can certainly use an anholonomic basis of, e.g., unit vectors.

Will this be fixed in Maple 16?

I misunderstood, I guess. I thought you were trying to covariantly differentiate vector fields on M. 

I suspect I still don't know quite what you are after. 

If you simply want to pullback a connection from M to S, you can do this with PushPullTensor applied to the connection on M. First argument should be a Transformation from N to S, with the expression of coordinates on S in terms those on M. Second argument should be the map (i) embedding S into M.

charlie

I misunderstood, I guess. I thought you were trying to covariantly differentiate vector fields on M. 

I suspect I still don't know quite what you are after. 

If you simply want to pullback a connection from M to S, you can do this with PushPullTensor applied to the connection on M. First argument should be a Transformation from N to S, with the expression of coordinates on S in terms those on M. Second argument should be the map (i) embedding S into M.

charlie