Re: Questions & Discussions on Vectors & relationships to differe ntia l geometry

[Jack Uretsky <jlu@HEP.ANL.GOV>]

Hi Joel-
        By S1 I mean the circle.
        Position on S1 is not a vector (in S1 although it might be
described by a vector in R^2).  Circular motion at constant speed -
the velocity vector lies in a tangent space and does not lie in S1,
right?  That's exactly what you were asking about, I thought.
        For homework, how do you describe the tangent space to S1.
        You have to be a litte careful, since S1 is unique among the
spheres Sn of dimension n.
                                Regards,
                                        Jack

On Thu, 15 Mar 2001, RAUBER, JOEL wrote:

> Jack,
>
> I'm not sure I understand your question.
>
> >         Why do you want to make things so complicated?  You
> > confront all
> > of these concepts when you consider circular motion.
>
> But my question came precisely from some musing on tranformations involving
> rotation plus translation and trying unravel what is geometric (coordinate
> independent) about vectors and what isn't invariant about them or the
> vectors we use to represent physical concepts, velocity for example.
>
> Joel Rauber

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