Mixing
Find a surface with given principal curvatures.
0
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I want to find a surface with principal curvatures at a point $k_1=2$, $k_2=-1$. Any idea how to find this?
differential-geometry
edited Jan 15 at 19:07
Mutantoe
612513
asked Jan 15 at 18:39
Giannis Giannis
1
$endgroup$
add a comment |
0
$begingroup$
I want to find a surface with principal curvatures at a point $k_1=2$, $k_2=-1$. Any idea how to find this?
differential-geometry
edited Jan 15 at 19:07
Mutantoe
612513
asked Jan 15 at 18:39
Giannis Giannis
1
$endgroup$
$begingroup$
You have to give an example of a surface that in some point the principal curvatures take that values, is that all?
$endgroup$
– Dog_69
Jan 15 at 18:44
$begingroup$
Welcome to MSE. What have you tried?
$endgroup$
– Ted Shifrin
Jan 15 at 19:21
$begingroup$
Take a hyperbolic paraboloid with saddle at the point. Play with the coefficients (semiaxes) to get the desired curvatures
$endgroup$
– GReyes
Jan 15 at 20:15
$begingroup$
@Dog_69 yes. this is a a past exam question so i ask if there is any method to answer these type of questions for any given principal curvatures
$endgroup$
– Giannis
Jan 15 at 22:13
$begingroup$
@Giannis Yes, there is. You should have seen the classification of the points according the principal curvatures and typical examples of surfaces for each case. In this case, you have $k_1>0$ and $k_2<0$ so at least you should be able to say that it is a hyperbolic point. What surface do you know that has hyperbolic points? Then, give the equation that describes the surface with those particular values may be rather more difficult. But still, if you have studied the typical surfaces, you should be able to reproduce GReyes reasoning.
$endgroup$
– Dog_69
Jan 15 at 22:50
add a comment |
0
0
0
$begingroup$
I want to find a surface with principal curvatures at a point $k_1=2$, $k_2=-1$. Any idea how to find this?
differential-geometry
edited Jan 15 at 19:07
Mutantoe
612513
asked Jan 15 at 18:39
Giannis Giannis
1
$endgroup$
I want to find a surface with principal curvatures at a point $k_1=2$, $k_2=-1$. Any idea how to find this?
differential-geometry
differential-geometry
edited Jan 15 at 19:07
Mutantoe
612513
asked Jan 15 at 18:39
Giannis Giannis
1
edited Jan 15 at 19:07
Mutantoe
612513
asked Jan 15 at 18:39
Giannis Giannis
1
edited Jan 15 at 19:07
Mutantoe
612513
edited Jan 15 at 19:07
Mutantoe
612513
edited Jan 15 at 19:07
Mutantoe
612513
612513
asked Jan 15 at 18:39
Giannis Giannis
1
asked Jan 15 at 18:39
Giannis Giannis
1
asked Jan 15 at 18:39
Giannis Giannis
1
1
$begingroup$
You have to give an example of a surface that in some point the principal curvatures take that values, is that all?
$endgroup$
– Dog_69
Jan 15 at 18:44
$begingroup$
Welcome to MSE. What have you tried?
$endgroup$
– Ted Shifrin
Jan 15 at 19:21
$begingroup$
Take a hyperbolic paraboloid with saddle at the point. Play with the coefficients (semiaxes) to get the desired curvatures
$endgroup$
– GReyes
Jan 15 at 20:15
$begingroup$
@Dog_69 yes. this is a a past exam question so i ask if there is any method to answer these type of questions for any given principal curvatures
$endgroup$
– Giannis
Jan 15 at 22:13
$begingroup$
@Giannis Yes, there is. You should have seen the classification of the points according the principal curvatures and typical examples of surfaces for each case. In this case, you have $k_1>0$ and $k_2<0$ so at least you should be able to say that it is a hyperbolic point. What surface do you know that has hyperbolic points? Then, give the equation that describes the surface with those particular values may be rather more difficult. But still, if you have studied the typical surfaces, you should be able to reproduce GReyes reasoning.
$endgroup$
– Dog_69
Jan 15 at 22:50
add a comment |
$begingroup$
You have to give an example of a surface that in some point the principal curvatures take that values, is that all?
$endgroup$
– Dog_69
Jan 15 at 18:44
$begingroup$
Welcome to MSE. What have you tried?
$endgroup$
– Ted Shifrin
Jan 15 at 19:21
$begingroup$
Take a hyperbolic paraboloid with saddle at the point. Play with the coefficients (semiaxes) to get the desired curvatures
$endgroup$
– GReyes
Jan 15 at 20:15
$begingroup$
@Dog_69 yes. this is a a past exam question so i ask if there is any method to answer these type of questions for any given principal curvatures
$endgroup$
– Giannis
Jan 15 at 22:13
$begingroup$
@Giannis Yes, there is. You should have seen the classification of the points according the principal curvatures and typical examples of surfaces for each case. In this case, you have $k_1>0$ and $k_2<0$ so at least you should be able to say that it is a hyperbolic point. What surface do you know that has hyperbolic points? Then, give the equation that describes the surface with those particular values may be rather more difficult. But still, if you have studied the typical surfaces, you should be able to reproduce GReyes reasoning.
$endgroup$
– Dog_69
Jan 15 at 22:50
$begingroup$
You have to give an example of a surface that in some point the principal curvatures take that values, is that all?
$endgroup$
– Dog_69
Jan 15 at 18:44
$begingroup$
You have to give an example of a surface that in some point the principal curvatures take that values, is that all?
$endgroup$
– Dog_69
Jan 15 at 18:44
$begingroup$
Welcome to MSE. What have you tried?
$endgroup$
– Ted Shifrin
Jan 15 at 19:21
$begingroup$
Welcome to MSE. What have you tried?
$endgroup$
– Ted Shifrin
Jan 15 at 19:21
$begingroup$
Take a hyperbolic paraboloid with saddle at the point. Play with the coefficients (semiaxes) to get the desired curvatures
$endgroup$
– GReyes
Jan 15 at 20:15
$begingroup$
Take a hyperbolic paraboloid with saddle at the point. Play with the coefficients (semiaxes) to get the desired curvatures
$endgroup$
– GReyes
Jan 15 at 20:15
$begingroup$
@Dog_69 yes. this is a a past exam question so i ask if there is any method to answer these type of questions for any given principal curvatures
$endgroup$
– Giannis
Jan 15 at 22:13
$begingroup$
@Dog_69 yes. this is a a past exam question so i ask if there is any method to answer these type of questions for any given principal curvatures
$endgroup$
– Giannis
Jan 15 at 22:13
$begingroup$
@Giannis Yes, there is. You should have seen the classification of the points according the principal curvatures and typical examples of surfaces for each case. In this case, you have $k_1>0$ and $k_2<0$ so at least you should be able to say that it is a hyperbolic point. What surface do you know that has hyperbolic points? Then, give the equation that describes the surface with those particular values may be rather more difficult. But still, if you have studied the typical surfaces, you should be able to reproduce GReyes reasoning.
$endgroup$
– Dog_69
Jan 15 at 22:50
$begingroup$
@Giannis Yes, there is. You should have seen the classification of the points according the principal curvatures and typical examples of surfaces for each case. In this case, you have $k_1>0$ and $k_2<0$ so at least you should be able to say that it is a hyperbolic point. What surface do you know that has hyperbolic points? Then, give the equation that describes the surface with those particular values may be rather more difficult. But still, if you have studied the typical surfaces, you should be able to reproduce GReyes reasoning.
$endgroup$
– Dog_69
Jan 15 at 22:50
add a comment |
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$begingroup$
You have to give an example of a surface that in some point the principal curvatures take that values, is that all?
$endgroup$
– Dog_69
Jan 15 at 18:44
$begingroup$
Welcome to MSE. What have you tried?
$endgroup$
– Ted Shifrin
Jan 15 at 19:21
$begingroup$
Take a hyperbolic paraboloid with saddle at the point. Play with the coefficients (semiaxes) to get the desired curvatures
$endgroup$
– GReyes
Jan 15 at 20:15
$begingroup$
@Dog_69 yes. this is a a past exam question so i ask if there is any method to answer these type of questions for any given principal curvatures
$endgroup$
– Giannis
Jan 15 at 22:13
$begingroup$
@Giannis Yes, there is. You should have seen the classification of the points according the principal curvatures and typical examples of surfaces for each case. In this case, you have $k_1>0$ and $k_2<0$ so at least you should be able to say that it is a hyperbolic point. What surface do you know that has hyperbolic points? Then, give the equation that describes the surface with those particular values may be rather more difficult. But still, if you have studied the typical surfaces, you should be able to reproduce GReyes reasoning.
$endgroup$
– Dog_69
Jan 15 at 22:50