ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 19 Aug 2016 15:08:07 +0200SageManifolds: raising and lowering Lorentzian indiceshttps://ask.sagemath.org/question/34453/sagemanifolds-raising-and-lowering-lorentzian-indices/In the reference manual of `SageManifolds` is shown how to calculate the `curvature_form` (pag. 407 of the reference).
However, the result is shown as $\Omega^a{}_b$, while I'd like to be able of manipulate the $\Omega^{ab}$.
**Question:**
How can the latter be defined?
Thank you.Fri, 12 Aug 2016 21:10:51 +0200https://ask.sagemath.org/question/34453/sagemanifolds-raising-and-lowering-lorentzian-indices/Comment by eric_g for <p>In the reference manual of <code>SageManifolds</code> is shown how to calculate the <code>curvature_form</code> (pag. 407 of the reference).</p>
<p>However, the result is shown as $\Omega^a{}_b$, while I'd like to be able of manipulate the $\Omega^{ab}$.</p>
<p><strong>Question:</strong>
How can the latter be defined?</p>
<p>Thank you.</p>
https://ask.sagemath.org/question/34453/sagemanifolds-raising-and-lowering-lorentzian-indices/?comment=34500#post-id-34500Since a and b are not tensor indices, but some labels for the set of curvature 2-forms, what do you mean by Omega^{ab} ?Wed, 17 Aug 2016 13:22:46 +0200https://ask.sagemath.org/question/34453/sagemanifolds-raising-and-lowering-lorentzian-indices/?comment=34500#post-id-34500Comment by Dox for <p>In the reference manual of <code>SageManifolds</code> is shown how to calculate the <code>curvature_form</code> (pag. 407 of the reference).</p>
<p>However, the result is shown as $\Omega^a{}_b$, while I'd like to be able of manipulate the $\Omega^{ab}$.</p>
<p><strong>Question:</strong>
How can the latter be defined?</p>
<p>Thank you.</p>
https://ask.sagemath.org/question/34453/sagemanifolds-raising-and-lowering-lorentzian-indices/?comment=34532#post-id-34532The `a` and `b` indices are indices in the tangent space. Which are raised and lowered with the flat metric (compatible with the signature of the curved spacetime). In my case $\eta = \rm{diag}( -1, 1, 1, 1)$, so $\Omega^1{}_0 = - \Omega^{10}$.Fri, 19 Aug 2016 15:08:07 +0200https://ask.sagemath.org/question/34453/sagemanifolds-raising-and-lowering-lorentzian-indices/?comment=34532#post-id-34532