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Jianbing_Shao's latest activity
J
Jianbing_Shao
replied to the thread
I
A sufficient condition for integrability of equation ##\nabla g=0##
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From your description I still can’t find the difference between Levi-Civita connection and teleparallel connection, If we start from a...
Aug 11, 2025
J
Jianbing_Shao
replied to the thread
I
A sufficient condition for integrability of equation ##\nabla g=0##
.
So in fact a metric field can be compatible with many different connections, and in them many have zero curvature, Then why a metric...
Aug 7, 2025
J
Jianbing_Shao
replied to the thread
I
A sufficient condition for integrability of equation ##\nabla g=0##
.
To a metrics ##g_{ab} = \eta_{IJ} {e_a}^{I} {e_b}^{J}##, it can be compatible with Levi-Civita connection with non-zero curvature. but...
Aug 6, 2025
J
Jianbing_Shao
replied to the thread
I
A sufficient condition for integrability of equation ##\nabla g=0##
.
If ##Q_{\alpha\mu\nu}= 0##, connection and metric field are compatible with each other, and if ##Q_{\alpha\mu\nu}\neq 0##, it means the...
Aug 4, 2025
J
Jianbing_Shao
replied to the thread
I
A sufficient condition for integrability of equation ##\nabla g=0##
.
In the paper you gave: He claimed: The failure of the connection to be metric is encoded in the non-metricity $$ Q_{\alpha\mu\nu}\equiv...
Aug 4, 2025
J
Jianbing_Shao
replied to the thread
I
A sufficient condition for integrability of equation ##\nabla g=0##
.
If you introduce additional terms, then I am not doubt that you can get a non-zero torsion. it is not strange. but if you didn't...
Aug 4, 2025
J
Jianbing_Shao
replied to the thread
I
A sufficient condition for integrability of equation ##\nabla g=0##
.
From the theorem I mentioned we can get the same result. Especially if the basis field ##e_a## is a coordinate basis, then curvature and...
Aug 3, 2025
J
Jianbing_Shao
posted the thread
I
A sufficient condition for integrability of equation ##\nabla g=0##
in
Special and General Relativity
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In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential...
Jul 10, 2025
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