This preview shows page 1. Sign up to view the full content.
Unformatted text preview: that satisFes the condition R 2 = x 2 + y 2 + z 2 + w 2 . Show that the metric on the 3sphere is given by ds 2 = dr 2 + R 2 sin 2 ( r/R )[ d 2 + sin 2 d 2 ]. The relation between x, y, z, w is x = R sin ( r/R ) sin cos , y = R sin ( r/R ) sin sin , z = R sin ( r/R ) cos , w = R cos ( r/R ). What are the natural ranges for r , and so that the 3sphere is covered exactly once? (You might Fnd it helpful to review the natural ranges of coordinates on the 2sphere.)...
View Full
Document
 Spring '10
 Lam
 Physics

Click to edit the document details