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Forums
Mathematics
Differential Geometry
Interior Product: Definition & Understanding
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[QUOTE="Silviu, post: 5838307, member: 588158"] Hello! The interior product is defined as ##i_X:\Omega^r(M)\to \Omega^{r-1}(M)##, with X being a vector on the manifold and ##\Omega^r(M)## the vector space of r-form at a point p on the manifold. Now for ##\omega \in \Omega^r(M) ## we have ##i_X\omega(X_1, ... X_{r-1}) = \omega (X,X_1, ... X_{r-1})##. I am not sure I understand it. Based on this definition, ##i_X## acts on an r-1 form and it turns it into an r-form, by making it acts on X, too. But by the definition in the first line, ##i_X## should act the other way around. What am I reading wrong here? Thank you! [/QUOTE]
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Mathematics
Differential Geometry
Interior Product: Definition & Understanding
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