Manuscript XI-A@1 · XI-A.tex · section · b8211ecc

Covariance of the invariant metric Euler operator

Covariance of the invariant metric Euler operator · lines 960–975

XI-A@1#eq:tensorpull

Let $F_{(2, 0), dens}^{*}$ denote pullback of a contravariant rank-two density of weight one:

(F_{(2, 0), dens}^{*} u)^{μν} (x) = det D F (x) (D F (x)^{- 1})^{μ}_{α} (D F (x)^{- 1})^{ν}_{β} \times u^{α β} (F (x)) .

All admitted flows preserve orientation.

Displayed formulas in this passage

XI-A@1#eq:tensorpull · line 965
$(F_{(2, 0), dens}^{*} u)^{μν} (x) = det D F (x) (D F (x)^{- 1})^{μ}_{α} (D F (x)^{- 1})^{ν}_{β} \times u^{α β} (F (x)) .$