Let wi and wa be k-forms defined on all of IR". Show that wi and wy have the same exterior derivative, that is, dwi = dw2, %3D if and only if Wi = w2 + dŋ for some (k – 1)-form 7 on R".
Let wi and wa be k-forms defined on all of IR". Show that wi and wy have the same exterior derivative, that is, dwi = dw2, %3D if and only if Wi = w2 + dŋ for some (k – 1)-form 7 on R".
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let wj and w2 be k-forms defined on all of R". Show that wi and wa have the same exterior derivative, that is,
dwi = dw2,
if and only if
Wi = w2 + dn
for some (k – 1)-form 7 on R".
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