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Unformatted text preview: p-forms and ( n-p )-forms dened by the Hodge star operator * : p n-p , that maps any p-form to a ( n-p )-form * dual to dened as follows. For each p-form the form * is the unique ( n-p )-form such that for any p-form * = h , i vol . In components, this means that ( * ) i p + 1 ... i n = 1 p ! i 1 ... i p i p + 1 ... i n p | g | g i 1 j 1 g i p j p j 1 ... j p = 1 p ! 1 p | g | g i p + 1 j p + 1 g i n j n j 1 ... j p j p + 1 ... j n j 1 ... j p . Recall that the Hodge star maps forms to pseudo-forms and vice-versa. Recall also that for any p-form , * 2 = (-1) p ( n-p ) , meaning that *-1 = (-1) p ( n-p ) * . di geom.tex; April 12, 2006; 17:59; p. 188...
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- Spring '10