Ric curvature and second fundamental form.
$begingroup$
Suppose $M$ is a minimal submanifod in $mathbb{R}^{n+1}$, by Gauss equation we have
$$operatorname{Ric}_Mgeq -|A|^2$$.
I have done similar calculations for surface in $mathbb{R}^3$. But it seems different, and here codimension is bigger than 1, I am kinda stuck. If anyone is familar with this calculation, could you show me some details?
riemannian-geometry
asked Jan 19 at 5:18
STUDENTSTUDENT
1207
$endgroup$
add a comment |
$begingroup$
Suppose $M$ is a minimal submanifod in $mathbb{R}^{n+1}$, by Gauss equation we have
$$operatorname{Ric}_Mgeq -|A|^2$$.
I have done similar calculations for surface in $mathbb{R}^3$. But it seems different, and here codimension is bigger than 1, I am kinda stuck. If anyone is familar with this calculation, could you show me some details?
riemannian-geometry
asked Jan 19 at 5:18
STUDENTSTUDENT
1207
$endgroup$
$begingroup$
What exactly are you trying to calculate?
$endgroup$
– Arctic Char
Jan 23 at 23:22
$begingroup$
Oh, I want to prove above inequality. But I have proved it myself after some help. Thanks for your interest.
$endgroup$
– STUDENT
Jan 25 at 1:50
add a comment |
$begingroup$
Suppose $M$ is a minimal submanifod in $mathbb{R}^{n+1}$, by Gauss equation we have
$$operatorname{Ric}_Mgeq -|A|^2$$.
I have done similar calculations for surface in $mathbb{R}^3$. But it seems different, and here codimension is bigger than 1, I am kinda stuck. If anyone is familar with this calculation, could you show me some details?
riemannian-geometry
asked Jan 19 at 5:18
STUDENTSTUDENT
1207
$endgroup$
Suppose $M$ is a minimal submanifod in $mathbb{R}^{n+1}$, by Gauss equation we have
$$operatorname{Ric}_Mgeq -|A|^2$$.
I have done similar calculations for surface in $mathbb{R}^3$. But it seems different, and here codimension is bigger than 1, I am kinda stuck. If anyone is familar with this calculation, could you show me some details?
riemannian-geometry
riemannian-geometry
asked Jan 19 at 5:18
STUDENTSTUDENT
1207
asked Jan 19 at 5:18
STUDENTSTUDENT
1207
asked Jan 19 at 5:18
STUDENTSTUDENT
1207
asked Jan 19 at 5:18
STUDENTSTUDENT
1207
asked Jan 19 at 5:18
STUDENTSTUDENT
1207
1207
$begingroup$
What exactly are you trying to calculate?
$endgroup$
– Arctic Char
Jan 23 at 23:22
$begingroup$
Oh, I want to prove above inequality. But I have proved it myself after some help. Thanks for your interest.
$endgroup$
– STUDENT
Jan 25 at 1:50
add a comment |
$begingroup$
What exactly are you trying to calculate?
$endgroup$
– Arctic Char
Jan 23 at 23:22
$begingroup$
Oh, I want to prove above inequality. But I have proved it myself after some help. Thanks for your interest.
$endgroup$
– STUDENT
Jan 25 at 1:50
$begingroup$
What exactly are you trying to calculate?
$endgroup$
– Arctic Char
Jan 23 at 23:22
$begingroup$
What exactly are you trying to calculate?
$endgroup$
– Arctic Char
Jan 23 at 23:22
$begingroup$
Oh, I want to prove above inequality. But I have proved it myself after some help. Thanks for your interest.
$endgroup$
– STUDENT
Jan 25 at 1:50
$begingroup$
Oh, I want to prove above inequality. But I have proved it myself after some help. Thanks for your interest.
$endgroup$
– STUDENT
Jan 25 at 1:50
add a comment |
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$begingroup$
What exactly are you trying to calculate?
$endgroup$
– Arctic Char
Jan 23 at 23:22
$begingroup$
Oh, I want to prove above inequality. But I have proved it myself after some help. Thanks for your interest.
$endgroup$
– STUDENT
Jan 25 at 1:50