Yrogirg
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 Apr2 accepted Why is $\frac{d}{d \mu} \big|_{\mu=0} \, F^*_\mu F^*_\lambda t = F^*_\lambda \frac{d}{d \mu} \big|_{\mu=0} \, F^*_\mu t$? Apr1 revised Why is $\frac{d}{d \mu} \big|_{\mu=0} \, F^*_\mu F^*_\lambda t = F^*_\lambda \frac{d}{d \mu} \big|_{\mu=0} \, F^*_\mu t$? title Dec9 awarded Caucus Nov25 comment Is there a codifferential for a covariant exterior derivative? mathoverflow.net/questions/97061/… seems to answer the question but it does not explain how to extend Hodge star to bundle valued differential forms. Nov25 answered If $\operatorname{Def} X = \frac{1}{2} \mathcal L_X g$ then what is $\operatorname{Def}^* \operatorname{Def} X$? Oct20 asked If $\operatorname{Def} X = \frac{1}{2} \mathcal L_X g$ then what is $\operatorname{Def}^* \operatorname{Def} X$? Oct16 accepted Can a bilinear map on smooth functions induce a bilinear map on tensor fields in this way? Oct15 comment Can a bilinear map on smooth functions induce a bilinear map on tensor fields in this way? to clarify terminology $(\alpha f + \beta g,h) = \alpha (f,h) + \beta (g,h)$ is linear over $\mathbb R$ if $\alpha, \beta \in \mathbb R$ (this one I meant) and over $C^\infty(M)$ if $\alpha, \beta \in C^\infty(M)$, right? Oct15 asked Can a bilinear map on smooth functions induce a bilinear map on tensor fields in this way? Oct6 accepted If $\operatorname{div} X = 0$ what can be said about $X^\flat$? Oct6 answered If $\operatorname{div} X = 0$ what can be said about $X^\flat$? Oct6 accepted Is there a Poincare lemma for codifferential? Oct6 revised Is there a codifferential for a covariant exterior derivative? added 313 characters in body Oct6 asked Is there a Poincare lemma for codifferential? Oct3 comment Is there a codifferential for a covariant exterior derivative? Oct3 comment Is there a codifferential for a covariant exterior derivative? mathoverflow.net/questions/142913/… seems to be related Oct3 comment Is there a codifferential for a covariant exterior derivative? Thank you. Right now even flat case would be nice. Do you have an explicit expression for $\delta^\nabla$? (it would probably require an extension of Hodge star operator). Oct3 comment Hodge decomposition on a manifold with a nontrivial connection Have you figured this out since the question was asked? Oct3 asked Is there a codifferential for a covariant exterior derivative? Oct1 accepted What is the scalar product of tensors?