Jianbing_Shao's latest activity
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.Yes, I think we should treat the metric compatible equation as differential equations. To do so we at least can understand two problems...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.Simply from a tetrad field , then we can calculate the difference between teleparallel connection and Levi-Civita connection: If we...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.Another problem ,Do you think a non trivial metric field can also be compatible with a zero curvature connection. they call it...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.Then return to the question we have discussed. From a non-zero curvature Levi-Civita connection and metric compatible equation, then how...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.In your definition, the fields ##e,\Gamma## is chosen independently. But if we demand that the connection ##\Gamma## to be the...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.Yes, I really think there is contradiction here, In the paper I quoted, He claimed that the holonomy group generated from a metric...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.Metric compatible equations and the equations you gave are two differential equations , In fact your equations is more complex, The...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.Because Levi-Civita connection is also compatible with metric. So it also satisfy the equation: ##\partial_a {e_b}^{I} = {\Gamma^c}_{ab}...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.I have read an interesting paper 'Conditions on a Connection to be a Metric Connection' by B. G. Schmidt(Commun. math. Phys. 29, 55—59...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.When we say the teleparallel connection ##\Gamma^{\alpha}_{\mu\nu} =e_a^{\alpha}\partial_{\mu}e^a_{\nu}## is flat , it has vanishing...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.To the equation above, I have a question: Because the equation above is a differential equations,, So even for equations like...
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JJianbing_Shao replied to the thread I A sufficient condition for integrability of equation ##\nabla g=0##.I read some papers about teleparallel connection. I have a question: When we introduce spin connection ##\omega^a_{\hphantom{a}\mu...