Notation about the curvature
0
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I'm reading an paper about geometry, I did not understand the notation (inequality):
$$Rmgeq K$$
where k is a real constant and $Rm$ is the curvature tensor. I don't understand what that notation means because $Rm$ is a 4-tensor.
differential-geometry
asked Jan 22 at 19:07
Miguel Angel Micky Huarachi SaMiguel Angel Micky Huarachi Sa
1
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add a comment |
0
$begingroup$
I'm reading an paper about geometry, I did not understand the notation (inequality):
$$Rmgeq K$$
where k is a real constant and $Rm$ is the curvature tensor. I don't understand what that notation means because $Rm$ is a 4-tensor.
differential-geometry
asked Jan 22 at 19:07
Miguel Angel Micky Huarachi SaMiguel Angel Micky Huarachi Sa
1
$endgroup$
$begingroup$
Maybe it would help if you added a link/reference to the paper
$endgroup$
– 0x539
Jan 22 at 19:31
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arxiv.org/abs/1005.3255 page 8 Theorem 2.5
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– Miguel Angel Micky Huarachi Sa
Jan 22 at 21:29
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They are saying all the sectional curvatures are bounded below by $K$.
$endgroup$
– Ted Shifrin
Jan 22 at 21:48
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Are you sure that is was $R_m$ and not $R_{nn}$? The latter would be the $(n,n)$ element of the Ricci curvature. Another possibility is that it is the scalar curvature, and the $m$ is some sort of label rather than an element index.
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– Paul Sinclair
Jan 23 at 3:08
add a comment |
0
0
0
$begingroup$
I'm reading an paper about geometry, I did not understand the notation (inequality):
$$Rmgeq K$$
where k is a real constant and $Rm$ is the curvature tensor. I don't understand what that notation means because $Rm$ is a 4-tensor.
differential-geometry
asked Jan 22 at 19:07
Miguel Angel Micky Huarachi SaMiguel Angel Micky Huarachi Sa
1
$endgroup$
I'm reading an paper about geometry, I did not understand the notation (inequality):
$$Rmgeq K$$
where k is a real constant and $Rm$ is the curvature tensor. I don't understand what that notation means because $Rm$ is a 4-tensor.
differential-geometry
differential-geometry
asked Jan 22 at 19:07
Miguel Angel Micky Huarachi SaMiguel Angel Micky Huarachi Sa
1
asked Jan 22 at 19:07
Miguel Angel Micky Huarachi SaMiguel Angel Micky Huarachi Sa
1
asked Jan 22 at 19:07
Miguel Angel Micky Huarachi SaMiguel Angel Micky Huarachi Sa
1
asked Jan 22 at 19:07
Miguel Angel Micky Huarachi SaMiguel Angel Micky Huarachi Sa
1
asked Jan 22 at 19:07
Miguel Angel Micky Huarachi SaMiguel Angel Micky Huarachi Sa
1
1
$begingroup$
Maybe it would help if you added a link/reference to the paper
$endgroup$
– 0x539
Jan 22 at 19:31
$begingroup$
arxiv.org/abs/1005.3255 page 8 Theorem 2.5
$endgroup$
– Miguel Angel Micky Huarachi Sa
Jan 22 at 21:29
$begingroup$
They are saying all the sectional curvatures are bounded below by $K$.
$endgroup$
– Ted Shifrin
Jan 22 at 21:48
$begingroup$
Are you sure that is was $R_m$ and not $R_{nn}$? The latter would be the $(n,n)$ element of the Ricci curvature. Another possibility is that it is the scalar curvature, and the $m$ is some sort of label rather than an element index.
$endgroup$
– Paul Sinclair
Jan 23 at 3:08
add a comment |
$begingroup$
Maybe it would help if you added a link/reference to the paper
$endgroup$
– 0x539
Jan 22 at 19:31
$begingroup$
arxiv.org/abs/1005.3255 page 8 Theorem 2.5
$endgroup$
– Miguel Angel Micky Huarachi Sa
Jan 22 at 21:29
$begingroup$
They are saying all the sectional curvatures are bounded below by $K$.
$endgroup$
– Ted Shifrin
Jan 22 at 21:48
$begingroup$
Are you sure that is was $R_m$ and not $R_{nn}$? The latter would be the $(n,n)$ element of the Ricci curvature. Another possibility is that it is the scalar curvature, and the $m$ is some sort of label rather than an element index.
$endgroup$
– Paul Sinclair
Jan 23 at 3:08
$begingroup$
Maybe it would help if you added a link/reference to the paper
$endgroup$
– 0x539
Jan 22 at 19:31
$begingroup$
Maybe it would help if you added a link/reference to the paper
$endgroup$
– 0x539
Jan 22 at 19:31
$begingroup$
arxiv.org/abs/1005.3255 page 8 Theorem 2.5
$endgroup$
– Miguel Angel Micky Huarachi Sa
Jan 22 at 21:29
$begingroup$
arxiv.org/abs/1005.3255 page 8 Theorem 2.5
$endgroup$
– Miguel Angel Micky Huarachi Sa
Jan 22 at 21:29
$begingroup$
They are saying all the sectional curvatures are bounded below by $K$.
$endgroup$
– Ted Shifrin
Jan 22 at 21:48
$begingroup$
They are saying all the sectional curvatures are bounded below by $K$.
$endgroup$
– Ted Shifrin
Jan 22 at 21:48
$begingroup$
Are you sure that is was $R_m$ and not $R_{nn}$? The latter would be the $(n,n)$ element of the Ricci curvature. Another possibility is that it is the scalar curvature, and the $m$ is some sort of label rather than an element index.
$endgroup$
– Paul Sinclair
Jan 23 at 3:08
$begingroup$
Are you sure that is was $R_m$ and not $R_{nn}$? The latter would be the $(n,n)$ element of the Ricci curvature. Another possibility is that it is the scalar curvature, and the $m$ is some sort of label rather than an element index.
$endgroup$
– Paul Sinclair
Jan 23 at 3:08
add a comment |
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$begingroup$
Maybe it would help if you added a link/reference to the paper
$endgroup$
– 0x539
Jan 22 at 19:31
$begingroup$
arxiv.org/abs/1005.3255 page 8 Theorem 2.5
$endgroup$
– Miguel Angel Micky Huarachi Sa
Jan 22 at 21:29
$begingroup$
They are saying all the sectional curvatures are bounded below by $K$.
$endgroup$
– Ted Shifrin
Jan 22 at 21:48
$begingroup$
Are you sure that is was $R_m$ and not $R_{nn}$? The latter would be the $(n,n)$ element of the Ricci curvature. Another possibility is that it is the scalar curvature, and the $m$ is some sort of label rather than an element index.
$endgroup$
– Paul Sinclair
Jan 23 at 3:08