Weighted integral formulas on manifolds |
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Authors: | Elin Götmark |
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Institution: | 1.Department of Mathematics,Chalmers University of Technology and G?teborg University,G?teborg,Sweden |
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Abstract: | We present a method of finding weighted Koppelman formulas for (p,q)-forms on n-dimensional complex manifolds X which admit a vector bundle of rank n over X×X, such that the diagonal of X×X has a defining section. We apply the method to ℙ
n
and find weighted Koppelman formulas for (p,q)-forms with values in a line bundle over ℙ
n
. As an application, we look at the cohomology groups of (p,q)-forms over ℙ
n
with values in various line bundles, and find explicit solutions to the -equation in some of the trivial groups. We also look at cohomology groups of (0,q)-forms over ℙ
n
×ℙ
m
with values in various line bundles. Finally, we apply our method to developing weighted Koppelman formulas on Stein manifolds. |
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Keywords: | |
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