(M,g) with M compact, tex2html_wrap109 , M Riemannian

Theorem:

tex2html_wrap110 tex2html_wrap111 unique decomposition tex2html_wrap112 where tex2html_wrap113 is harmonic. tex2html_wrap114 . This can also be written using the laplacian as tex2html_wrap115 .

tex2html_wrap116 . This can be inverted to get tex2html_wrap117 as long as there are no 0 mode oscillations.

Uniqueness

Can define a projection operator tex2html_wrap129 . Then use projection operator to solve for tex2html_wrap130 , then show that you can invert to get tex2html_wrap131 .

Consequences




source
psfile jl@crush.caltech.edu index
kahler_Hodge_decomposition_theorem