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I don't understand why a mapping of phi(x,y)=(x/y,sqrt(x2+y2)) can be an enveloping space for the above curve?

Any ideas, anyone?

- Thread starter maddy
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- #1

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I don't understand why a mapping of phi(x,y)=(x/y,sqrt(x2+y2)) can be an enveloping space for the above curve?

Any ideas, anyone?

- #2

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this doesn t quite make sense. if you draw a curve in ROriginally posted by maddy

How do you draw a curve with line element ds2=y2dx2+dy2 in a R2 space? Is it just lots of x=a lines, with a-any real number?

this metric is

[tex]

ds = \sqrt{1+\left(\frac{df}{dx}\right)^2}dx

[/tex]

from the euclidean metric

[tex]

ds^2 = dx^2 + dy^2

[/tex]

i cannot get the line element you wrote from a curve in euclidean R

what is an enveloping space? i have never heard this term before. can you define it please?I don't understand why a mapping of phi(x,y)=(x/y,sqrt(x2+y2)) can be an enveloping space for the above curve?

Any ideas, anyone?

- #3

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It's from this paper gr-qc/9405063.what is an enveloping space? i have never heard this term before. can you define it please?

Can I substitute make x'=arctan(y/x) and y'=sqrt(x2+y2) into ds2=dx2+dy2 so that phi'(x,y)=(x',y') be the covering space for the original Euclidean space with (0,0) removed?this doesn't quite make sense. if you draw a curve in R2, it inherits an induced metric from the normal euclidean metric.

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