AN ANALYTIC PROOF OF RIEMANN-ROCH HIRZEBRUCH THEOREM FOR KAEHLER MANIFOLDS
V. K. Patodi · WORLD SCIENTIFIC eBooks · 1996
feme/ (d β : C~(ζ 9 ) -> C°°(ζ Q+1 )) and B e = image (d 2 : C°°(ζ q -1 ) -• C°°(ζ)), 0 C°°(ζ 0 )) -codim (image of d 2 + d* g : C°°(ζ e ) -> C TO (ζ 0 )) .The adjoint of the operator d 2 + d* 2 : C°°(ζ e ) -* C°°(ζ°) is the operator d 2 + d* 2 : C°°(ζ 0 ) -^ C°°(ζ e ) and we have (d 2 + rf* g )W, + d* g ) = d f d* f + dV.= -4 , J 2 being the complex analogue of the Laplace-Beltrame operator.The operator Δ 2 is a self-adjoint elliptic operator from C°°(ζ q ) -> C°°(ζ Q ), 0 ί.Then the following proposition is an immediate consequence of an argument due to Atiyah Bott; see [4, §3].