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mentioned two basic properties at Hodge star operator (namely those needed at holographic principle ;-)
The definition wasn’t general enough for your properties, so I generalised it.
Thanks, Toby. Do you mean the paragraph “Generalizations”?
No, I mean my first edit, the basic Definition. Already that was a very restricted context.
I have expanded a bit more, making the Hodge inner product more explicit, and making explicit the two versions: with values in $C^\infty(X)$ and after integration against $vol$ with values in $\mathbb{R}$.
Am not convinced yet that the $\langle-,-\rangle$-versus-$(-\mid-)$-notation is good, but will leave it at that for the moment.
added a pointer to the basic fact regarding the action on Kähler manifolds, also at Kähler manifold itself
The link to the action on Kähler manifolds is broken.
Thanks, fixed now.
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