Transformation on surface patches that preserves length of curves.
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suppose $mathcalS subset mathbbR^3$ is a surface patch, and let $mathcalC$ a simple curve on $mathcalS$, suppose $f$ is a transformation/function/mapping such that $f(mathcalS) = mathcalS'$ with the property that for any $mathcalC$ we have $length(f(mathcalC)) = length(C)$.
Folding a piece of paper for example I guess would have this property.
But anyway, I'm not an expert in differential geometry but do these transformations here have a name, is there any study about transformations that have such property?
I need some name for references so I can look it up.
Thank you
(Again, I'm not an expert in differential geometry, but I do know "elementary differential geometry").
differential-geometry reference-request definition
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up vote
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suppose $mathcalS subset mathbbR^3$ is a surface patch, and let $mathcalC$ a simple curve on $mathcalS$, suppose $f$ is a transformation/function/mapping such that $f(mathcalS) = mathcalS'$ with the property that for any $mathcalC$ we have $length(f(mathcalC)) = length(C)$.
Folding a piece of paper for example I guess would have this property.
But anyway, I'm not an expert in differential geometry but do these transformations here have a name, is there any study about transformations that have such property?
I need some name for references so I can look it up.
Thank you
(Again, I'm not an expert in differential geometry, but I do know "elementary differential geometry").
differential-geometry reference-request definition
Such a map is called a (local) isometry. Actually the definition of an isometry is different, but your assumption implies the the map is an isometry (locally).
â Thomas
Aug 8 at 18:09
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
suppose $mathcalS subset mathbbR^3$ is a surface patch, and let $mathcalC$ a simple curve on $mathcalS$, suppose $f$ is a transformation/function/mapping such that $f(mathcalS) = mathcalS'$ with the property that for any $mathcalC$ we have $length(f(mathcalC)) = length(C)$.
Folding a piece of paper for example I guess would have this property.
But anyway, I'm not an expert in differential geometry but do these transformations here have a name, is there any study about transformations that have such property?
I need some name for references so I can look it up.
Thank you
(Again, I'm not an expert in differential geometry, but I do know "elementary differential geometry").
differential-geometry reference-request definition
suppose $mathcalS subset mathbbR^3$ is a surface patch, and let $mathcalC$ a simple curve on $mathcalS$, suppose $f$ is a transformation/function/mapping such that $f(mathcalS) = mathcalS'$ with the property that for any $mathcalC$ we have $length(f(mathcalC)) = length(C)$.
Folding a piece of paper for example I guess would have this property.
But anyway, I'm not an expert in differential geometry but do these transformations here have a name, is there any study about transformations that have such property?
I need some name for references so I can look it up.
Thank you
(Again, I'm not an expert in differential geometry, but I do know "elementary differential geometry").
differential-geometry reference-request definition
asked Aug 8 at 17:01
user8469759
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1,3041514
Such a map is called a (local) isometry. Actually the definition of an isometry is different, but your assumption implies the the map is an isometry (locally).
â Thomas
Aug 8 at 18:09
add a comment |Â
Such a map is called a (local) isometry. Actually the definition of an isometry is different, but your assumption implies the the map is an isometry (locally).
â Thomas
Aug 8 at 18:09
Such a map is called a (local) isometry. Actually the definition of an isometry is different, but your assumption implies the the map is an isometry (locally).
â Thomas
Aug 8 at 18:09
Such a map is called a (local) isometry. Actually the definition of an isometry is different, but your assumption implies the the map is an isometry (locally).
â Thomas
Aug 8 at 18:09
add a comment |Â
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Such a map is called a (local) isometry. Actually the definition of an isometry is different, but your assumption implies the the map is an isometry (locally).
â Thomas
Aug 8 at 18:09