Do Carmo 3.4. exercise 8: Vector Field on a Surface The Next CEO of Stack OverflowKilling vector field of the sphereLocal Reparametrization of Surface using known Vector Field (Differential Geometry)Computing the differental of an orthogonal projectionHarmonic coordinate functions in minimal surfacesDifferential Geometry Regular Surface problemTerms of the derivative of vector field on a regular surface restricted to a curve [from Do Carmo]Do Carmo's Definition of a Vector FieldJohn Lee problem: Vector field conservative if and only if it is a gradient fieldDerive the representation of a vector field in a parametrization of a regular surfacedo carmo 3.4 exercise 5
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Do Carmo 3.4. exercise 8: Vector Field on a Surface
The Next CEO of Stack OverflowKilling vector field of the sphereLocal Reparametrization of Surface using known Vector Field (Differential Geometry)Computing the differental of an orthogonal projectionHarmonic coordinate functions in minimal surfacesDifferential Geometry Regular Surface problemTerms of the derivative of vector field on a regular surface restricted to a curve [from Do Carmo]Do Carmo's Definition of a Vector FieldJohn Lee problem: Vector field conservative if and only if it is a gradient fieldDerive the representation of a vector field in a parametrization of a regular surfacedo carmo 3.4 exercise 5
$begingroup$
I'm having trouble trying to start this. Here is the problem statement:
Show that if $w : S to mathbbR^3$ is a differentiable vector field on a regular surface $S subset mathbbR^3$, and $w(p) neq 0$ for some $p in S$, then it is possible to parametrize a neihghborhood of $p$ by $x(u,v)$ in such a way that $x_u = w$.
How do I start this? What do I need to show to prove this?
differential-geometry vector-fields parametrization
asked Mar 18 at 11:08
JB071098JB071098
347212
$endgroup$
This question had a bounty worth +50
reputation from JB071098 that ended ended at 2019-03-28 06:35:02Z">19 hours ago. Grace period ends in 4 hours
This question has not received enough attention.
add a comment |
$begingroup$
I'm having trouble trying to start this. Here is the problem statement:
Show that if $w : S to mathbbR^3$ is a differentiable vector field on a regular surface $S subset mathbbR^3$, and $w(p) neq 0$ for some $p in S$, then it is possible to parametrize a neihghborhood of $p$ by $x(u,v)$ in such a way that $x_u = w$.
How do I start this? What do I need to show to prove this?
differential-geometry vector-fields parametrization
asked Mar 18 at 11:08
JB071098JB071098
347212
$endgroup$
This question had a bounty worth +50
reputation from JB071098 that ended ended at 2019-03-28 06:35:02Z">19 hours ago. Grace period ends in 4 hours
This question has not received enough attention.
1
$begingroup$
It would be helpful to give more context. What, specifically, do you not understand in the question? Where are you stuck?
$endgroup$
– Joshua Mundinger
Mar 23 at 14:49
$begingroup$
@JoshuaMundinger I'm not sure what steps would be necessary in order to prove this. "it is possible to parametrize... in a way such that $x_u=w$ " makes me think that this is a question of existence, but if that is the case, I don't know how to show it exists.
$endgroup$
– JB071098
Mar 23 at 14:55
1
$begingroup$
The main theorem of Section 3.4 in do Carmo's Differential Geometry of Curves and Surfaces is exactly a theorem of existence of some type. What is the difference between the text's results and your problem? This may help you get started so that we can give more specific help.
$endgroup$
– Joshua Mundinger
Mar 24 at 1:36
add a comment |
$begingroup$
I'm having trouble trying to start this. Here is the problem statement:
Show that if $w : S to mathbbR^3$ is a differentiable vector field on a regular surface $S subset mathbbR^3$, and $w(p) neq 0$ for some $p in S$, then it is possible to parametrize a neihghborhood of $p$ by $x(u,v)$ in such a way that $x_u = w$.
How do I start this? What do I need to show to prove this?
differential-geometry vector-fields parametrization
asked Mar 18 at 11:08
JB071098JB071098
347212
$endgroup$
I'm having trouble trying to start this. Here is the problem statement:
Show that if $w : S to mathbbR^3$ is a differentiable vector field on a regular surface $S subset mathbbR^3$, and $w(p) neq 0$ for some $p in S$, then it is possible to parametrize a neihghborhood of $p$ by $x(u,v)$ in such a way that $x_u = w$.
How do I start this? What do I need to show to prove this?
differential-geometry vector-fields parametrization
differential-geometry vector-fields parametrization
asked Mar 18 at 11:08
JB071098JB071098
347212
asked Mar 18 at 11:08
JB071098JB071098
347212
edited Mar 21 at 6:46
JB071098
asked Mar 18 at 11:08
JB071098JB071098
347212
asked Mar 18 at 11:08
JB071098JB071098
347212
asked Mar 18 at 11:08
JB071098JB071098
347212
347212
This question had a bounty worth +50
reputation from JB071098 that ended ended at 2019-03-28 06:35:02Z">19 hours ago. Grace period ends in 4 hours
This question has not received enough attention.
This question had a bounty worth +50
reputation from JB071098 that ended ended at 2019-03-28 06:35:02Z">19 hours ago. Grace period ends in 4 hours
This question has not received enough attention.
1
$begingroup$
It would be helpful to give more context. What, specifically, do you not understand in the question? Where are you stuck?
$endgroup$
– Joshua Mundinger
Mar 23 at 14:49
$begingroup$
@JoshuaMundinger I'm not sure what steps would be necessary in order to prove this. "it is possible to parametrize... in a way such that $x_u=w$ " makes me think that this is a question of existence, but if that is the case, I don't know how to show it exists.
$endgroup$
– JB071098
Mar 23 at 14:55
1
$begingroup$
The main theorem of Section 3.4 in do Carmo's Differential Geometry of Curves and Surfaces is exactly a theorem of existence of some type. What is the difference between the text's results and your problem? This may help you get started so that we can give more specific help.
$endgroup$
– Joshua Mundinger
Mar 24 at 1:36
add a comment |
1
$begingroup$
It would be helpful to give more context. What, specifically, do you not understand in the question? Where are you stuck?
$endgroup$
– Joshua Mundinger
Mar 23 at 14:49
$begingroup$
@JoshuaMundinger I'm not sure what steps would be necessary in order to prove this. "it is possible to parametrize... in a way such that $x_u=w$ " makes me think that this is a question of existence, but if that is the case, I don't know how to show it exists.
$endgroup$
– JB071098
Mar 23 at 14:55
1
$begingroup$
The main theorem of Section 3.4 in do Carmo's Differential Geometry of Curves and Surfaces is exactly a theorem of existence of some type. What is the difference between the text's results and your problem? This may help you get started so that we can give more specific help.
$endgroup$
– Joshua Mundinger
Mar 24 at 1:36
1
1
$begingroup$
It would be helpful to give more context. What, specifically, do you not understand in the question? Where are you stuck?
$endgroup$
– Joshua Mundinger
Mar 23 at 14:49
$begingroup$
It would be helpful to give more context. What, specifically, do you not understand in the question? Where are you stuck?
$endgroup$
– Joshua Mundinger
Mar 23 at 14:49
$begingroup$
@JoshuaMundinger I'm not sure what steps would be necessary in order to prove this. "it is possible to parametrize... in a way such that $x_u=w$ " makes me think that this is a question of existence, but if that is the case, I don't know how to show it exists.
$endgroup$
– JB071098
Mar 23 at 14:55
$begingroup$
@JoshuaMundinger I'm not sure what steps would be necessary in order to prove this. "it is possible to parametrize... in a way such that $x_u=w$ " makes me think that this is a question of existence, but if that is the case, I don't know how to show it exists.
$endgroup$
– JB071098
Mar 23 at 14:55
1
1
$begingroup$
The main theorem of Section 3.4 in do Carmo's Differential Geometry of Curves and Surfaces is exactly a theorem of existence of some type. What is the difference between the text's results and your problem? This may help you get started so that we can give more specific help.
$endgroup$
– Joshua Mundinger
Mar 24 at 1:36
$begingroup$
The main theorem of Section 3.4 in do Carmo's Differential Geometry of Curves and Surfaces is exactly a theorem of existence of some type. What is the difference between the text's results and your problem? This may help you get started so that we can give more specific help.
$endgroup$
– Joshua Mundinger
Mar 24 at 1:36
add a comment |
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1
$begingroup$
It would be helpful to give more context. What, specifically, do you not understand in the question? Where are you stuck?
$endgroup$
– Joshua Mundinger
Mar 23 at 14:49
$begingroup$
@JoshuaMundinger I'm not sure what steps would be necessary in order to prove this. "it is possible to parametrize... in a way such that $x_u=w$ " makes me think that this is a question of existence, but if that is the case, I don't know how to show it exists.
$endgroup$
– JB071098
Mar 23 at 14:55
1
$begingroup$
The main theorem of Section 3.4 in do Carmo's Differential Geometry of Curves and Surfaces is exactly a theorem of existence of some type. What is the difference between the text's results and your problem? This may help you get started so that we can give more specific help.
$endgroup$
– Joshua Mundinger
Mar 24 at 1:36