This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: pforms and ( np )forms dened by the Hodge star operator * : p np , that maps any pform to a ( np )form * dual to dened as follows. For each pform the form * is the unique ( np )form such that for any pform * = 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 pseudoforms and viceversa. Recall also that for any pform , * 2 = (1) p ( np ) , meaning that *1 = (1) p ( np ) * . di geom.tex; April 12, 2006; 17:59; p. 188...
View Full
Document
 Spring '10
 Wong
 Geometry

Click to edit the document details