inner product, hodge dual def

[Orbots]

This is might help resolve tension between vee and inner product. NecroMonster — Yesterday at 6:22 AM however, a "dot product" is essentially an operation mapping a vector to a covector (the musical isomorphism defined by the metric) and the contraction with another vector

[Orbots]

hamish_todd — Yesterday at 6:29 AM But if you're doing differential geometry and you're using vectors and covectors then you almost certainly have a metric? NecroMonster — Yesterday at 6:31 AM if you want to have a levi-civita connection? yeah but you dont have to differential geometry is doable without a metric structure